1.1 Principal, Interest, Time

A. Introduction to Simple Interest

Many business interactions involve borrowing and lending money. The fee that is charged to compensate the lender is called interest. In other words, interest is the rent paid for an amount of money borrowed. When the amount is returned, interest is added to the original amount borrowed or invested.

Interest may be calculated in two different ways:

• Simple Interest: the interest is calculated only on the initial amount borrowed or invested. With this method, the growth of money is linear, meaning it increases at a constant rate. Simple interest is typically applied to short-term financial products, such as short-term personal loans and treasury bills.
• Compound Interest: the interest earned in earlier periods, such as previous months, is added to the principal amount. This accumulated total then earns interest in subsequent periods. As a result, money grows exponentially, or at an increasingly rapid rate, under compound interest. This method is commonly applied to long-term financial products like mortgages and car loans.

In simple interest, the interest charged is based on a percentage of the original amount borrowed or invested. The total interest amount depends on three key factors:

• How much: the principal, which is the initial sum of money borrowed or invested.
• How long: the duration for which the money is borrowed or invested.
• What rate: the interest rate applied to the principal

For example, consider the principal amount of $100 invested at a simple interest rate of 10% per annum (i.e., year) for two years.

• At the end of the first year, the interest is calculated as 10% of $100, resulting in $10.
• At the end of the second year, the interest remains 10% of the original principal, again amounting to $10.

Therefore, over the two years, the initial investment of $100 grows to $120, as illustrated in Figure 1.1.1.

Figure 1.1.1 The amount of simple interest on a $100 investment at the interest of 10% p.a.

B. Computing the Simple Interest

The amount of simple interest is given by

 [asciimath]I=P*r*t[/asciimath] Formula 1.1

Here [asciimath]P[/asciimath] is the principal amount (present value), [asciimath]r[/asciimath] the interest rate expressed in percent, and [asciimath]t[/asciimath] is the time period for which the principal amount is borrowed or invested.

When applying the simple interest formula, ensure the time period ([asciimath]t[/asciimath]) matches the time period of the interest rate ([asciimath]r[/asciimath]). For instance, if the interest rate is given per year (per annum or p.a.), you must convert the time to years before using it in the formula. Similarly, if the interest rate is monthly or daily, convert the time to months or days, respectively.

To convert the number of days to the equivalent number of years, divide by 365 since a year typically has 365 days. For converting months into years, divide the number of months by 12, as a year contains 12 months, as shown in Figure 1.1.2. Additionally, if you are given two specific dates, calculate the ‘Days Between Dates’ (DBD) to find out the number of days for the time period.

Figure 1.1.2 How to convert the number of days and months to the number of years

Computing the Principal, Time, and Interest Rate