If you have a lot of surplus cash, it would hardly make sense to hide it under your mattress or bury it in the backyard of your townhouse. As any investment specialist will tell you, you want your money to work for you instead of just sitting idle. So you can invest and be rewarded by earning interest.

Do you know if your account at the Royal Bank of Canada (RBC) has paid you the right amount of interest? You might assume that because everything at a bank is fully automated it is guaranteed to be correct. However, ultimately all automation at the Royal Bank relies on input by an employee. What if your interest rate is keyed in wrong? Maybe the computer programmer erred in a line of computer code and the amount of interest is miscalculated. What if RBC had a computer glitch? These pitfalls highlight the importance of always checking your account statements.

In business, it would be rare for an organization to borrow or lend money for free. That is not to say that businesses are ruthless with each other; in the previous chapter, you saw that most business transactions are completed through interest-free credit transactions involving invoicing. However, this generosity does not extend indefinitely. After the credit period elapses, the business essentially treats an unpaid invoice as a loan and starts charging an interest penalty.

When businesses need to borrow money, promissory notes, demand loans, and commercial papers are just three of the possibilities discussed later in this chapter.

Even governments need to borrow money. Have you ever thought about how the government of Canada or your provincial government goes about doing that? While a government has many methods at its disposal, a common method is to use treasury bills—in essence, borrowing the money from investors.

On a personal level, almost all people invest and borrow money at some time. This chapter examines consumer lines of credit and student loans, both of which carry simple interest rates. On the earnings side, it is common for people to have savings accounts that earn low rates of interest. Other short-term investments include treasury bills, commercial papers, and short-term guaranteed investment certificates (GICs).

The bottom line is that money does not come free. In this chapter, you will explore the concept of simple interest, learn how to calculate it, and then apply simple interest to various financial tools.

6.1 Principal, Rate, Time

Your investments may be at risk if stock and bond markets slump, as a story in the Globe and Mail predicts. You wonder if you should shift your money into relatively secure short-term investments until the market booms again. You consider your high-interest savings account, but realize that only the first $60,000 of your savings account is insured. Perhaps you should put some of that money into treasury bills instead.

Looking ahead, what income will you live on once you are no longer working? As your career develops, you need to save money to fund your lifestyle in retirement. Some day you will have $100,000 or more that you must invest and reinvest to reach your financial retirement goals.

To make such decisions, you must first understand how to calculate simple interest. Second, you need to understand the characteristics of the various financial options that use simple interest. Armed with this knowledge, you can make smart financial decisions!

The world of finance calculates interest in two different ways:

1. Simple Interest. A simple interest system primarily applies to short-term financial transactions, with a time frame of less than one year. In this system, which is explored in this chapter, interest accrues but does not compound.
2. Compound Interest. A compound interest system primarily applies to long-term financial transactions, with a time frame of one year or more. In this system, which the next chapter explores, interest accrues and compounds upon previously earned interest.

Simple Interest

In a simple interest environment, you calculate interest solely on the amount of money at the beginning of the transaction. When the term of the transaction ends, you add the amount of the simple interest to the initial amount. Therefore, throughout the entire transaction the amount of money placed into the account remains unchanged until the term expires. It is only on this date that the amount of money increases. Thus, an investor has more money or a borrower owes more money at the end.

The figure illustrates the concept of simple interest. In this example, assume $1,000 is placed into an account with 12% simple interest for a period of 12 months. For the entire term of this transaction, the amount of money in the account always equals $1,000. During this period, interest accrues at a rate of 12%, but the interest is never placed into the account. When the transaction ends after 12 months, the $120 of interest and the initial $1,000 are then combined to total $1,120.

A loan or investment always involves two parties—one giving and one receiving. No matter which party you are in the transaction, the amount of interest remains unchanged. The only difference lies in whether you are earning or paying the interest.

• If you take out a personal loan from a bank, the bank gives you the money and you receive the money. In this situation, the bank earns the simple interest and you are being charged simple interest on your loan. In the figure, this means you must pay back not only the $1,000 you borrowed initially but an additional $120 in interest.
• If you place your money into an investment account at the bank, you have given the money and the bank has received the money. In this situation, you earn the simple interest on your money and the bank pays simple interest to your investment account. In the figure, this means the bank must give you back your initial $1,000 at the end plus an additional $120 of interest earned.

The Formula

The best way to understand how simple interest is calculated is to think of the following relationship:

Amount of simple interest = How much at What simple interest rate for How long

Notice that the key variables are the amount, the simple interest rate, and time. Formula 6.1 combines these elements into a formula for simple interest.

Simple Interest

Important Notes

Recall that algebraic equations require all terms to be expressed with a common unit. This principle remains true for Formula 6.1, particularly with regard to the interest rate and the time period. For example, if you have a 3% annual interest rate for nine months, then either

• The time needs to be expressed annually as 9/12 of a year to match the yearly interest rate, or
• The interest rate needs to be expressed monthly as 3%/12 = 0.25% per month to match the number of months.
  

Paths To Success

Four variables are involved in the simple interest formula, which means that any three can be known, requiring you to solve for the fourth missing variable. To reduce formula clutter, the triangle technique illustrated here helps you remember how to rearrange the formula as needed.

Give It Some Thought

1. If you have money in your savings account (or any other investment) and it earns simple interest over a period of time, would you have more or less money in your account in the future?
2. If you have a debt for which you haven’t made any payments, yet it is being charged simple interest on the principal, would you owe more or less money in the future?

Solutions:

1. More, because the interest is earned and therefore is added to your savings account.

2. More, because you owe the principal and you owe the interest, which increases your total amount owing.

Example 6.1A: How Much Interest Is Owed?

Julio borrowed $1,100 from Maria five months ago. When he first borrowed the money, they agreed that he would pay Maria 5% simple interest. If Julio pays her back today, how much interest does he owe her?
Calculate the amount of interest that Julio owes Maria (I).
What You Already Know Step 1: The terms of their agreement are as follows: P = $1,100           r = 5%                  t = 5 months	How You Will Get There Step 2: The rate is annual, and the time is in months. Convert the time to an annual number. Step 3: Apply Formula 6.1.
Step 2: Five months out of 12 months in a year is of a year, or t = Step 3: I = $1,100 × 5% × = $1,100 × 0.05 × = $22.92
For Julio to pay back Maria, he must reimburse her for the $1,100 principal borrowed plus an additional $22.92 of simple interest as per their agreement.

Example 6.1B: Do You Know Your Interest Rate?

A $3,500 investment earned $70 of interest over the course of six months. What annual rate of simple interest did the investment earn?
Calculate the annual interest rate (r).
What You Already Know Step 1: The principal, interest amount, and time are known: P = $3,500         I = $70                t = 6 months	How You Will Get There Step 2: The computed interest rate needs to be annual, so you must express the time period annually as well. Step 3: Apply Formula 6.1, rearranging for r.
Step 2: Six months out of 12 months in a year is of a year, or t = Step 3: $70 = $3,500 × r ×   or 4%
For $3,500 to earn $70 simple interest over the course of six months, the annual simple interest rate must be 4%.

Time and Dates

In the examples of simple interest so far, the time period equalled an exact number of months. While this is convenient in many situations, financial institutions and organizations calculate interest based on the exact number of days in the transaction, which changes the interest amount.

To illustrate this, assume you had money saved for the entire months of July and August, where t = or t = 0.1 of a year. However, if you use the exact number of days, the 31 days in July and 31 days in August total 62 days. In a 365-day year that is t = % 

or t = 0.169863 of a year. Notice a difference of 0.003196 occurs. Therefore, to be precise in performing simple interest calculations, you must calculate the exact number of days involved in the transaction.

Figuring Out the Days

In practice, when counting the number of days in a transaction you include the first day but not the last day. This is because interest is calculated on the daily closing balance, not on interim balances throughout a day. For example, if you borrowed $500 on June 3 and paid it back with interest on June 5, the closing balance on June 3 and June 4 is $500. However, on June 5 a zero balance is restored. Therefore, you count June 3 and 4 as days of interest but not June 5, so you will owe two days of interest, not three.

There are three common ways to calculate the number of days involved in a transaction.

Method 1: Use Your Knuckles

You can use your knuckles as an aid to remembering which months of the year have more or fewer days.

Put your knuckles side by side and start on your outermost knuckle. Every knuckle represents a month with 31 days. Every valley between the knuckles represents a month that does not have 31 days (30 in all except February, which has 28 or 29). Now start counting months. Your first knuckle (pinkie finger) is January, which has 31 days. Next is your first valley, which is February and it does not have 31 days. Your next knuckle (ring finger) is March, which has 31 days … and so on. When you get to your last knuckle (your index finger), move to the other hand’s first knuckle (an index finger again). Notice that July and August are the two months back to back with 31 days.

If you are trying to calculate the number of days between March 20 and May 4, use your knuckles to recall that March has 31 days and April has 30 days. The calculations are illustrated in the table here.

Why does the end date of one line become the start date of the next line? Recall that you count the first day, but not the last day. Therefore, on the first line March 31 has not been counted yet and must be counted on the second line. Ultimately a transaction extending from March 20 to May 4 involves 45 days as the time period.

Method 2: Use A Table of Serial Numbers

In the table on the next page, the days of the year are assigned a serial number. The number of days between any two dates in the same calendar year is simply the difference between the serial numbers for the dates.

Using the example in Method 1, when the dates are within the same calendar year, find the serial number for the later date, May 4 (Day 124) and the serial number for the earlier date, March 20 (Day 79). Then, find the difference between the two serial numbers (124 – 79 = 45 days).

*For Leap years, February 29 becomes Day 60 and the serial number for each subsequent day is increased by 1.

Method 3: Use The BAII Plus Date Function

Your BAII Plus calculator is programmed with the ability to calculate the number of days involved in a transaction according to the principle of counting the first day but not the last day. The function “Date” is located on the second shelf above the number one. To use this function, open the window by pressing 2nd 1.

• Scroll amongst the four display lines by using your ↑ and ↓ arrows. There are four variables:

1. DT1 is the starting date of the transaction.
2. DT2 is the ending date of the transaction.
3. DBD is the days between dates, which is your t in Formula 6.1.

4. ACT or 360 is the method of calculating the days between dates. In ACT (for “actual”), the calculator calculates the DBD based on the correct number of days in the month. In 360, the DBD is based on treating every month as having 30 days (30 × 12 = 360 days). For all calculations, set the calculator to the ACT mode. Toggle this setting by pressing 2nd SET.

• To enter a date into the calculator, the calculator uses the format of MM.DDYY where:
• MM is the numerical value of the month; you do not need to enter the leading zero on months with only one digit.
• DD is the day of the month; you must always enter this value with two digits using a leading zero for days 1 through 9 in a month.
• YY is the last two digits of the year; you must always enter this with two digits. If your question does not involve a year, select an appropriate year of your choice.
• As long as you know any two of the DT1, DT2, or DBD variables, you can calculate the third. Enter any two of the three variables, pressing ENTER after each and ensuring the window shows the output variable you are seeking, and then press CPT.

Using the example in Method 1, to calculate the time from March 20 to May 4 you first need to choose a year arbitrarily, perhaps 2011. Therefore, perform the following sequence:

2nd DATE

2nd CLR Work (to erase previous calculations)

3.2011 ENTER ↓ (this is March 20, 2011)

5.0411 ENTER ↓ (this is May 4, 2011)

CPT

Answer: 45

Note that the answer is the same as the one you arrived at manually using your knuckles.

Important Notes

When solving for t, decimals may appear in your solution. For example, if calculating t in days, the answer may show up as 45.9978 or 46.0023 days; however, interest is calculated only on complete days. This occurs because the interest amount (I) used in the calculation has been rounded off to two decimals. Since the interest amount is imprecise, the calculation of t is imprecise. When this occurs, round t off to the nearest integer.

Things To Watch Out For

Miscalculating the number of days in February has to be one of the most common errors. To help you remember how many days are in February, recall your knowledge of leap years.

• February has 28 days except for leap years, in which it has 29 days.
• Leap years are those years that are evenly divisible by four or 400. However, those years that are evenly divisible by 100 (excepting years that are evenly divisible by 400) are not leap years. Here are some examples to illustrate this rule:

1. The year 1900 was not a leap year, since it is evenly divisible by 100 and not by 400.
2. The year 1996 was a leap year, since it is evenly divisible by four and not by 100.
3. The year 2000 was one of those exception years, and it was a leap year since it is evenly divisible by 400.
4. The year 2004 was once again a leap year since it is evenly divisible by four and not by 100. Thus, in this century 2004, 2008, 2012, 2016, 2020, 2024, and so on by fours are all leap years with 29 days.
5. The year 2100 will not be a leap year, since it is evenly divisible by 100.

Note that when it comes to the total number of days in a year, simple interest calculations ignore the 366th day in a leap year. Therefore, assume a year has 365 days in all calculations.

Paths To Success

When entering two dates either on the calculator or in Excel, the order in which you key in the dates is not important. If you happen to put the last day of the transaction into the first field (DT1 or Start Date) and the start day of the transaction into the last field (DT2 or End Date), then the number of days will compute as a negative number since the dates are reversed. Ignore the negative sign in these instances. Using the example, on your calculator if you had keyed May 4 into DT1 and March 20 into DT2, the DBD computes as −45, in which you ignore the negative sign to determine the answer is 45 days.

Example 6.1E: Time Using Dates

Azul borrowed $4,200 from Hannah on November 3, 2011. Their agreement required Azul to pay back the loan on April 14, 2012, with 8% simple interest. In addition to the principal, how much interest does Azul owe Hannah on April 14?
Calculate the amount of simple interest (I) that Azul owes Hannah on his loan.
What You Already Know Step 1: The principal, simple interest rate, and dates are known: P = $4,200         r = 8%                  Start Date = November 3, 2011       End Date = April 14, 2012	How You Will Get There Step 1 (continued): Calculate the number of days in the transaction. Note that this transaction involves February 2012, which is a leap year. Step 2: The rate is annual and the time is in days. Convert the time to an annual number. Step 3: Apply Formula 6.1.
Step 1 (continued): Start Date End Date Days between Dates November 3, 2011 November 30, 2011 30 − 3 = 27 November 30, 2011 December 31, 2011 31 − 0 = 31 December 31, 2011 January 31, 2012 31 − 0 = 31 January 31, 2012 February 29, 2012 29 − 0 = 29 February 29, 2012 March 31, 2012 31 − 0 = 31 March 31, 2012 April 14, 2012 14 − 0 = 14 TOTAL 27 + 31 + 31 + 29 + 31 + 14 = 163 days Step 2: 163 days out of 365 days in a year is t = Step 3: I = $4,200 × 8% × = $4,200 × 0.08 × 0.446575 = $150.05
Azul borrowed the money for a period of 163 days and owes Hannah $150.05 of simple interest on his loan, in addition to repaying the principal of $4,200.

 Calculator Instructions

 

Variable Interest Rates

Not all interest rates remain constant. There are two types of interest rates:

1. Fixed. A fixed interest rate is an interest rate that is unchanged for the duration of the transaction.
2. Variable. A variable interest rate is an interest rate that is open to fluctuations over the duration of a transaction. This variable interest rate is usually tied to the prime rate, which is an interest rate set by the Bank of Canada that usually forms the lowest lending rate for the most secure loans. Most people and companies are usually charged the prime rate plus a percentage (typically 0.5% to 5%) to arrive at the variable interest rate. The Bank of Canada periodically adjusts this rate because of economic and financial considerations in Canada.

In all of the previous examples in this section, the interest rate (r) was fixed for the duration of the transaction. When r fluctuates, you must break the question into time periods or time fragments for each value of r. In each of these time fragments, you calculate the amount of simple interest earned or charged and then sum the interest amounts to form the total interest earned or charged.

This figure illustrates this process with a variable rate that changes twice in the course of the transaction. To calculate the total interest amount, you need to execute Formula 6.1 for each of the time fragments. Then total the interest amounts from each of the three time fragments to calculate the interest amount (I) for the entire transaction.

Example 6.1G: A Floating Rate

Julio borrowed $10,000 on May 17 at a variable interest rate of prime + 3% when the prime rate was 2¼%. On June 22 the prime rate increased by ¼%, and on September 2 it increased again by ½%. How much interest will Julio pay when he repays his loan on October 4?
Calculate the amount of interest that Julio owes for the entire time frame of his loan, or I, from May 17 to October 4.
What You Already Know Step 1: There is an initial interest rate and then it changes twice over the course of the transaction. That means there are three time periods and three different interest rates. The principal is also known: P = $10,000. Date Interest Rate May 17 to June 22 2¼% + 3% = 5¼% June 22 to September 2 5¼% + ¼% = 5½% September 2 to October 4 5½% + ½% = 6%	How You Will Get There Step 1 (continued): Calculate the number of days for each of the three time periods. Step 2: The rates are annual while each of the times are in days. Convert each of the times to an annual number. Step 3: For each time period, apply Formula 6.1. Step 3 (continued): Sum the three interest amounts to arrive at the total interest paid.
Step 1 (continued) Step 2 Step 3 Dates Calculations Total # of Days Convert t to annual Calculate interest May 17 to June 22 May 17 to May 31 = 14 days May 31 to June 22 = 22 days 14 + 22 = 36 days     June 22 to September 2 June 22 to June 30 = 8 days June 30 to July 31 = 31 days July 31 to August 31 = 31 days August 31 to Sept 2 = 2 days 8 + 31 + 31 + 2 = 72 days   September 2 to October 4 Sept 2 to Sept 30 = 28 days Sept 30 to October 4 = 4 days 28 + 4 = 32 days   %   Step 3 (continued): TOTAL $319.32
Calculator Instructions
Julio owes $319.32 of simple interest on his October 4 repayment date.

Calculator Instructions

6.2 Moving Money Involving Simple Interest

Can you calculate the amount of money required to meet a future goal? Assume you will graduate college with your business administration diploma in a few months and have already registered at your local university to continue with your studies toward a bachelor of commerce degree. You estimate your total tuition, fees, and textbooks at $8,000. After investigating some short-term investments, you find the best simple rate of interest obtainable is 4.5%. How much money must you invest today for it to grow with interest to the needed tuition money?

In the previous section, you calculated the amount of interest earned or charged on an investment or loan. While this number is good to know, most of the time investors are interested solely in how much in total, including both principal and interest, is either owed or saved. Also, to calculate the interest amount in Formula 6.1, you must know the principal. When people plan for the future, they know the future amount of money that they need but do not know how much money they must invest today to arrive at that goal. This is the case in the opening example above, so you need a further technique for handling simple interest.

This section explores how to calculate the principal and interest together in a single calculation. It adds the flexibility of figuring out how much money there is at the beginning of the time period so long as you know the value at the end, or vice versa. In this way, you can solve almost any simple interest situation.

Maturity Value (or Future Value)

The maturity value of a transaction is the amount of money resulting at the end of a transaction, an amount that includes both the interest and the principal together. It is called a maturity value because in the financial world the termination of a financial transaction is known as the “maturing” of the transaction. The amount of principal with interest at some point in the future, but not necessarily the end of the transaction, is known as the future value.

Depending on the financial scenario, what information you know, and what variable you need to calculate, you may need a second formula offering an alternative method of calculating the simple interest dollar amount.

Things To Watch Out For

As with Formula 6.1, the most common mistake in the application of Formula 6.2 is failing to ensure that the rate and time are expressed in the same units. Before you proceed, always check these two variables!

Paths To Success

When solving Formula 6.2 for either rate or time, it is generally easier to use Formulas 6.3 and 6.1 instead. Follow these steps to solve for rate or time:

• If you have been provided with both the present value and future value, apply Formula 6.3 to calculate the amount of interest (I).
• Apply and rearrange Formula 6.1 to solve for either rate or time as required.

Give It Some Thought

In each of the following situations, determine which statement is correct.

• If you have a future value of $5,000 and interest is involved, then your present value is
• More than $5,000
• The same
• Less than $5,000
• If you had a principal of $10,000 earning 10% simple interest for any period less than a year, you earn
• More than $1,000 interest
• Exactly $1,000 interest
• Less than $1,000 interest
• If you took out a loan for $2,500 at a 5% simple interest rate for six months and you made no payments during that time frame, you owe
• More than $2,500
• Exactly $2,500
  Solutions: Less than $5,000. When being charged or earning interest, the present value is always less than the future value. Less than $1,000 interest. The $10,000 earns exactly $1,000 interest per year, so any time frame less than a year produces a smaller interest amount.More than $2,500. When interest is being charged, the future value is always larger than the present value.
  Less than $2,500

   

Equivalent Payments

Life happens. Sometimes the best laid financial plans go unfulfilled. Perhaps you have lost your job. Maybe a reckless driver totalled your vehicle, which you now have to replace at an expense you must struggle to fit into your budget. No matter the reason, you find yourself unable to make your debt payment as promised.

On the positive side, maybe you just received a large inheritance unexpectedly. What if you bought a scratch ticket and just won $25,000? Now that you have the money, you might want to pay off that debt early. Can it be done?

Whether paying late or paying early, any amount paid must be equivalent to the original financial obligation. As you have learned, when you move money into the future it accumulates simple interest. When you move money into the past, simple interest must be removed from the money. This principle applies both to early and late payments:

• Late Payments. If a debt is paid late, then a financial penalty that is fair to both parties involved should be imposed. That penalty should reflect a current rate of interest and be added to the original payment. Assume you owe $100 to your friend and that a fair current rate of simple interest is 10%. If you pay this debt one year late, then a 10% late interest penalty of $10 should be added, making your debt payment $110. This is no different from your friend receiving the $100 today and investing it himself at 10% interest so that it accumulates to $110 in one year.
• Early Payments. If a debt is paid early, there should be some financial incentive (otherwise, why bother?). Therefore, an interest benefit, one reflecting a current rate of interest on the early payment, should be deducted from the original payment. Assume you owe your friend $110 one year from now and that a fair current rate of simple interest is 10%. If you pay this debt today, then a 10% early interest benefit of $10 should be deducted, making your debt payment today $100. If your friend then invests this money at 10% simple interest, one year from now he will have the $110, which is what you were supposed to pay.

Notice in these examples that a simple interest rate of 10% means $100 today is the same thing as having $110 one year from now. This illustrates the concept that two payments are equivalent payments if, once a fair rate of interest is factored in, they have the same value on the same day. Thus, in general you are finding two amounts at different points in time that have the same value, as illustrated in the figure below.

 Paths To Success

Being financially smart means paying attention to when you make your debt payments. If you receive no financial benefit for making an early payment, then why make it? The prudent choice is to keep the money yourself, invest it at the best interest rate possible, and pay the debt off when it comes due. Whatever interest is earned is yours to keep and you still fulfill your debt obligations in a timely manner!

6.3 Application: Savings Accounts and Short-Term GICs

When the stock market offers potentially huge returns, why would anyone put money into an investment that earns just a few percent annually? The answer of course is that sometimes stocks decrease in value. For example, after reaching a historic high in June 2008, the Toronto Stock Exchange plunged 40% over the course of the next six months. So if you are not willing to take the risk in the stock market, there are many options for investing your money that are safe and secure, particularly savings accounts and short-term guaranteed investment certificates (GICs). Some of the benefits and drawbacks associated with safe and secure investments are listed in the table below.

Savings Accounts

A savings account is a deposit account that bears interest and has no stated maturity date. These accounts are found at most financial institutions, such as commercial banks (Royal Bank of Canada, TD Canada Trust, etc.), trusts (Royal Trust, Laurentian Trust, etc.), and credit unions (FirstOntario, Steinbach, Assiniboine, Servus, etc.). Owners of such accounts make deposits to and withdrawals from these accounts at any time, usually accessing the account at an automatic teller machine (ATM), at a bank teller, or through online banking.

A wide variety of types of savings accounts are available. This textbook focuses on the most common features of most savings accounts, including how interest is calculated, when interest is deposited, insurance against loss, and the interest rate amounts available.

1. How Interest Is Calculated. There are two common methods for calculating simple interest:
2. Accounts earn simple interest that is calculated based on the daily closing balance of the account. The closing balance is the amount of money in the account at the end of the day. Therefore, any balances in the account throughout a single day do not matter. For example, if you start the day with $500 in the account and deposit $3,000 at 9:00 a.m., then withdraw the $3,000 at 4:00 p.m., your closing balance is $500. That is the principal on which interest is calculated, not the $3,500 in the account throughout the day.
3. Accounts earn simple interest based on a minimum monthly balance in the account. For example, if in a single month you had a balance in the account of $900 except for one day, when the balance was $500, then only the $500 is used in calculating the entire month’s worth of interest.
4. When Interest Is Deposited. Interest is accumulated and deposited (paid) to the account once monthly, usually on the first day of the month. Thus, the interest earned on your account for the month of January appears as a deposit on February 1.
5. Insurance against Loss. Canadian savings accounts at commercial banks are insured by the national Canada Deposit Insurance Corporation (CDIC), which guarantees up to $100,000 in savings. At credit unions, this insurance is usually provided provincially by institutions such as the Deposit Insurance Corporation of Ontario (DICO), which also guarantees up to $100,000. This means that if your bank were to fold, you could not lose your money (so long as your deposit was within the maximum limit). Therefore, savings accounts carry almost no risk.
6. Interest Rate Amounts. Interest rates are higher for investments that are riskier. Savings accounts carry virtually no risk, which means the interest rates on savings accounts tend to be among the lowest you can earn. At the time of writing, interest rates on savings accounts ranged from a low of 0.05% to a high of 1.95%. Though this is not much, it is better than nothing and certainly better than losing money!

While a wide range of savings accounts are available, these accounts generally follow one of two common structures when it comes to calculating interest. These structures are flat rate savings accounts and tiered savings accounts. Each of these is discussed separately.

Short-Term Guaranteed Investment Certificates (GICs)

A guaranteed investment certificate (GIC) is an investment that offers a guaranteed rate of interest over a fixed period of time. In many countries around the world, a GIC is often called a time or term deposit. GICs are found mostly at commercial banks, trust companies, and credit unions. Just like savings accounts, they have a very low risk profile and tend to have much lower rates than are available through other investments such as the stock market or bonds. They are also unconditionally guaranteed, much like savings accounts. In this section, you will deal only with short-term GICs, defined as those that have a time frame of less than one year.

The table below summarizes three factors that determine the interest rate on a short-term GIC: principal, time, and redemption privileges.

Amount of Principal. Typically, a larger principal is able to realize a higher interest rate than a smaller principal.

1. 1. Time. The length of time that the principal is invested affects the interest rate. Short-term GICs range from 30 days to 364 days in length. A longer term usually realizes higher interest rates.
   2. Redemption Privileges. The two types of GICs are known as redeemable and nonredeemable. A redeemable GIC can be cashed in at any point before the maturity date, meaning that you can access your money any time you want it. A nonredeemable GIC “locks in” your money for the agreed-upon term. Accessing that money before the end of the term usually incurs a stiff financial penalty, either on the interest rate or in the form of a financial fee. Nonredeemable GICs carry a higher interest rate.

Chapter 6 Case Study

Managing A Company’s Investments

The Situation

As with most mid-size to large companies, Lightning Wholesale has a finance department to manage its money. The structure of Lightning Wholesale’s financial plan allows each department to have its own bank account from which all expenses, purchases, and charges are deducted. This same account has all revenues and interest deposited into it.

The manager of the sporting goods department wants a summary of all interest amounts earned or charged to her department for the year 2013. This will allow her to better understand and assess the financial policies of the company and make any necessary changes for 2014.

The Data

(All numbers in thousands of dollars)

Important Information

• The balance in the sporting goods bank account on December 31, 2012, was $2,245,636.45.
• The bank account permits a negative balance, which the bank treats as an operating loan. The interest rate on any operating loan is prime + 0.5%. Accrued interest is placed into the account on the last day of each month.
• When a positive balance exists, the bank pays interest at 0.85% on the first $50,000 in the account and 1.2% only on the portion above $50,000. Interest is deposited on the last day of each month.
• On the last day of each month, the finance department purchases T-bills in the market that will mature by the last day of the next month. The face value of T-bills are bought in denominations of exactly $100,000 in a quantity as permitted by the current balance in the bank account. If the bank account has a negative balance (i.e., it is using its operating loan), no T-bills are purchased that month. For example, if the bank account has a balance of $350,000 on March 31, three $100,000 T-bills will be purchased with 30 days left to maturity.
• Assume all revenues are deposited to the account at the end of the corresponding month.
• Assume all cost of goods sold and operating expenses are deducted at the end of the corresponding month.
• For simplicity, assume the balance in the bank account remains unchanged throughout each month.

Your Tasks

The manager wants a report that summarizes the following information from December 31, 2012, to December 31, 2013:

• The total interest earned through T-bill investments.
• The total interest earned from the bank account.
• The total interest charged by any operating loans.
• The final balance in the bank account as of December 31, 2013, when no purchases of T-bills for January 2014 have been made.

In order to meet the manager’s requirements, work through 2013 month by month starting from December 31, 2012, by following the steps below. Once arriving at December 31, 2013, use the answers to provide the four pieces of information requested by the manager.

• Using the opening balance, determine the face value of T-bills that can be purchased. If the balance is negative, no T-bills are purchased, so skip to step 4.
• Calculate the purchase price of the T-bills using the current market yield and the number of days until the end of the next month. The difference between the purchase price and the face value is the total interest earned for the month by T-bills.
• Deduct the purchase price of the T-bills from the balance in the account.
• Examine the account balance.
• If the balance is positive, calculate the interest earned for the month based on the tiered interest rate structure. This is the total interest earned by the investment for the month.
• If the balance is negative, charge interest to the account for the month using the interest rate charged by the bank. This is the total interest charged by the operating loan for the month.
• To figure out the balance at the end of the next month, take the balance from step 4, add the face value of the T-bills that are maturing at the end of the month, add any interest earned from the bank account (step 4a), deduct any interest charged on the operating loan (step 4b), add the revenues for the month, and deduct the expenses and cost of goods sold for the month.
• Go back to step 1 and repeat for the next month.
• When all months are complete, calculate the required totals and present the requested summary information to the manager.