3.5 Demand Loans

LEARNING OBJECTIVES

  • Use simple interest in solving problems involving demand loans.

Almost everybody needs a little financial help from time to time. Perhaps you want to purchase a big-ticket item like a big-screen 3D HDTV but do not have the cash in full today to pay for it up front. However, the television is drastically on sale this week and if you wait to purchase it you will lose out and potentially have to pay full price next month. Or maybe as you flip through all of your bills you notice that though you will eventually have enough income to cover them, some of your payments fall due a few days before you will actually receive your income. What will you do for those few days until the income is deposited into your account?

Businesses also find themselves in similar situations. Maybe a supplier is offering a special deal on a product line, but the business does not have the cash to stock up. Also typical of business operations is that they make purchases in advance of sales, so they need to spend the money before they can receive the revenue to pay for their expenses. How can a business get access to short-term financing?

Demand Loans

A demand loan is a short-term loan that generally has no specific maturity date, where the borrower can make a payment to settle the loan, either in part or full, at any time without any interest penalty, and where the lender can demand repayment in full at any time. A demand loan allows borrowing when needed and repayment when money permits, subject to the following characteristics.

  1. Credit Limit. This establishes the maximum amount that can be borrowed.
  2. Variable Interest Rate. Almost all demand loans use variable simple interest rates based on the prime rate. Only the best, most secure customers can receive prime, while others usually get “prime plus” some additional amount.
  3. Fixed Interest Payment Date. Interest is always payable on the same date each and every month. For simplicity, the payment is usually tied to a chequing or savings account, allowing the interest payment to occur automatically.
  4. Interest Calculation Procedure. Interest is always calculated using a simple interest procedure based on the daily closing balance in the account. This means the first day but not the last day is counted.
  5. Security. Loans can be secured or unsecured. Secured loans are those loans that are guaranteed by an asset such as a building or a vehicle. In the event that the loan defaults, the asset can be seized by the lender to pay the debt. Unsecured loans are those loans backed up by the general goodwill and nature of the borrower. Usually a good credit history or working relationship is needed for these types of loans. A secured loan typically enables access to a higher credit limit than an unsecured loan.
  6. Repayment Structure. The repayment of the loan is either variable or fixed.
    • A variable repayment structure allows the borrower to repay any amount at any time, although a minimum requirement may have to be met such as “at least 2% of the current balance each month.” A current balance is the balance in an account plus any accrued interest. Accrued interest is any interest amount that has been calculated but not yet placed (charged or earned) into an account.
    • A fixed repayment structure requires a fixed payment amount toward the current balance on the same date each and every month.

Some examples of demand loans include:

  1. Personal Line of Credit (LOC). A demand loan for individuals, a personal line of credit is generally unsecured and is granted to those individuals who have high credit ratings and an established relationship with a financial institution. Because a line of credit is unsecured, the credit limit is usually a small amount, such as $10,000. Repayment is variable and usually has a minimum monthly requirement based on the current balance.
  2. Home Equity Line of Credit (HELOC). This is a special type of line of credit for individuals that is secured by residential homeownership. Typically, an amount not exceeding 80% of the equity in a home is used to establish the credit limit, thus enabling an individual access to a large amount of money. The interest rates tend to follow mortgage interest rates and are lower than personal lines of credit. Repayment is variable, usually involving only the accrued interest every month.
  3. Operating Loans. An operating loan is the business version of a line of credit. An operating loan may or may not be secured, depending on the nature of the business and the strength of the relationship the business has with the financial institution. Repayment can be either variable or fixed.
  4. Student Loans. A loan available to students to pursue educational opportunities. Although these are long-term in nature, the calculation of interest on a student loan uses simple interest techniques. These loans are not true demand loans because a student loan cannot be called in at any time. Repayment is fixed monthly.

EXAMPLE

Jesse received a $8500 demand loan from her bank at 4% simple interest.  Three months later, the interest rate on the loan increased to 4.3% simple interest.  Jesse repaid the loan in full eight months after taking out the loan.  What is the total amount of interest that Jesse paid on the loan?

Solution:

Step 1:  Calculate the amount of interest, [latex]I[/latex], for the first three months when the interest rate is 4%.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 8500 \times 0.04 \times \frac{3}{12} \\ & = & \$85 \end{eqnarray*}[/latex]

Step 2:  Calculate the amount of interest, [latex]I[/latex], for the last five months when the interest rate is 4.3%.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 8500 \times 0.043 \times \frac{5}{12} \\ & = & \$152.29 \end{eqnarray*}[/latex]

Step 3:  Find the total interest.

[latex]\begin{eqnarray*} \mbox{Total Interest} & = & 85+152.29 \\ & = & \$237.29  \end{eqnarray*}[/latex]

The total amount of interest that Jesse paid on the loan was $237.29.

TRY IT

On March 17, 2023, Mark took out a $10,000 demand loan at 3.1% simple interest.  On May 29, 2023, the interest rate changed to 2.3% simple interest and on July 31, 2023, the interest rate changed to 2.7%.  Mark repaid the loan on September 3, 2023.  How much interest did Mark pay on the loan?

 

Click to see Solution

 

Interest from March 17 to May 29.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 10,000 \times 0.031 \times \frac{73}{365} \\ & = & \$62 \end{eqnarray*}[/latex]

Interest from May 29 to  July 31.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 10,000 \times 0.023 \times \frac{63}{365} \\ & = & \$39.70 \end{eqnarray*}[/latex]

Interest from July 31 to September 3.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 10,000 \times 0.027 \times \frac{34}{365} \\ & = & \$25.15 \end{eqnarray*}[/latex]

Total interest.

[latex]\begin{eqnarray*} \mbox{Total Interest} & = & 62+39.70+25.15 \\ & = & \$126.85  \end{eqnarray*}[/latex]

Partial Payments of Demand Loans

The borrower can make partial payments on a demand loan at any time, without penalty, to reduce the outstanding balance on the loan.  When a partial payment is made, the payment is first used to reduce the interest on the loan.  If the interest is completely paid off by the payment, then the remainder of the payment is applied to reduce the principal on the loan. This approach is called the declining balance method.

NOTE

A partial payment may be more or less than the interest that is due on the loan at the time the payment is made.  Each time a partial payment is made, the interest due at the time of the payment is calculated.

  • If the partial payment is larger than the amount of interest due, then the interest is paid first and any remaining amount from the payment is used to reduce the principal.
  • If the partial payment is smaller than the amount of interest due, then the entire payment is applied to interest due. Any interest that is not paid-off by the payment is carried forward to the next payment. Because there is nothing leftover from the payment, nothing is applied to the principal.

EXAMPLE

Sarah received a demand loan of $20,000 on April 2, 2023 at 7% simple interest.  She made a partial payment of $100 on May 19, 2023 and another payment of $3,000 on June 17, 2023.  She paid-off the loan on August 5, 2023.  Calculate the final payment Sarah made on August 5, 2023 to clear the loan.

Solution:

Step 1:  Calculate the amount of interest, [latex]I[/latex], due at the time of first payment on May 19, 2023.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 20,000 \times 0.07 \times \frac{47}{365} \\ & = & \$180.27 \end{eqnarray*}[/latex]

Step 2:  Apply the payment on May 19, 2023 to the interest due.  Because the payment is smaller than the interest due, there is an interest balance that must be carried forward to the next payment.

[latex]\begin{eqnarray*} \mbox{Interest Balance} & = & 180.27-100 \\ & = & \$80.27 \end{eqnarray*}[/latex]

Step 3:  Calculate the amount of interest, [latex]I[/latex], due at the time of the second payment on June 17, 2023 .

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 20,000 \times 0.07 \times \frac{29}{365} \\ & = & \$111.23 \end{eqnarray*}[/latex]

Step 4:  Apply the payment on June 17, 2023 to the interest due, including the unpaid interest from the previous payment.  Calculate the leftover amount from the payment after paying the interest.

[latex]\begin{eqnarray*} \mbox{Leftover Amount from Payment} & = & 3,000-(80.27+111.23) \\ & = & \$2808.50  \end{eqnarray*}[/latex]

Step 5:  Apply the leftover amount from the June 17, 2023 payment to the loan principal.

[latex]\begin{eqnarray*}  \mbox{Principal Remaining} & = & 20,000-2,808.50 \\ & = & \$17,191.50 \end{eqnarray*}[/latex]

Step 6:  Calculate the amount of interest, [latex]I[/latex], due on August 5, 2023.  Note that interest is only charged on the remaining principal from the last payment.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 17,191.50 \times 0.07 \times \frac{49}{365} \\ & = & \$161.55 \end{eqnarray*}[/latex]

Step 7:  To clear the loan on August 5, 2023, the remaining principal and the interest due must both be paid.

[latex]\begin{eqnarray*}  \mbox{Final Payment} & = & 17,191.50+161.55 \\ & = & \$17,353.05 \end{eqnarray*}[/latex]

The clear the loan on August 5, 2023, Sarah must make a final payment of $17,353.05.

TRY IT

Tom took out a $8,000 demand loan at 5%.  Three months after he took out the loan Tom repaid $1,000 towards the loan and eight months after he took out the loan Tom repaid $3,500 towards the loan.  Tom cleared the loan fourteen months after he took out the loan.  Calculate the size of Tom’s final payment.

 

Click to see Solution

 

Balance after the $1,000 payment in 3 months.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 8,000 \times 0.05 \times \frac{3}{12} \\ & = & \$100 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} \mbox{Leftover Amount from Payment} & = & 1,000-100 \\ & = & \$900 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} \mbox{Principal Remaining} & = & 8,000-900 \\ & = & \$7,100 \end{eqnarray*}[/latex]

Balance after the $3,500 payment in 8 months.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 7,100 \times 0.05 \times \frac{5}{12} \\ & = & \$147.92 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*}\mbox{Leftover Amount from Payment} & = & 3,500-147.92 \\ & = & \$3,352.08 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} \mbox{Principal Remaining} & = & 7,100-3,352.08 \\ & = & \$3,747.92 \end{eqnarray*}[/latex]

Final payment in 14 months.

[latex]\begin{eqnarray*} I & = & P \times r \times t \\ & = & 3,747.92 \times 0.05 \times \frac{6}{12} \\ & = & \$93.70 \\ \\   \mbox{Final Payment} & = & 3,747.92+93.70 \\ & = & \$3,841.62 \end{eqnarray*}[/latex]

Repayment Schedules

A repayment schedule is a table that details the financial transactions in an account including the balance, interest amounts, and payments/advances. The table below presents the table structure used for setting up a repayment schedule.  Each number in the table corresponds to an entry below that explains how to use each column or row.

Balance Before Transaction ([latex]P[/latex]) Annual Interest Rate ([latex]r[/latex]) Number of Days ([latex]t[/latex]) Interest Charged ([latex]I[/latex]) Accrued Interest Payment or Advance Principal Amount Balance After Transaction
Start Date (1)
(2) (3) (4) (5) (6) (7) (8) (9) (10)
  1. The first row appears if the schedule has an opening balance. In these instances, list the start date in the first column and the opening balance in the last column.
  2. List the date of any transaction. This could include a payment, advance, interest rate change, or an accrued interest payment.
  3. Carry this number forward from (1) (the balance after the transaction from the previous row).
  4. Record the interest rate that applies to the date interval in the first column.
  5. Calculate the number of days between the date on the previous row and the current row. Use the financial calculator’s date function to count the number of days. Express the number annually to match the interest rate (i.e. divide the number of days by 365).
  6. Compute the interest charges for the date interval using [latex]I = P \times r \times t[/latex]. Use (3), (4), and (5) as your values for the formula.
  7. Enter the cumulative total of any unpaid or accrued interest as of the current row’s date. This amount is the sum of (6) from the current row plus any number recorded in this column from the row above.
  8. Enter the amount of the transaction occurring for this row of the table. Payments should be recorded as positives (credits) as they will decrease the balance, and advances should be recorded as negatives (debits) as they will increase the balance. If this is an interest payment date, one of the following two events will happen. Regardless of which event happens, cross out the accrued interest amount in (7) as it is considered paid, so the accrued interest balance is reduced to zero once again.
    1. Only the interest payment occurs on this date. Copy the accrued interest from (7) into this column.
    2. An additional payment or advance is made on this date. Add the accrued interest to the advance or payment, placing the sum into this column.
  9. One of two events will happen in this column.
    1. On an interest payment date, subtract the accrued interest from the amount in (8).
    2. On a date other than an interest payment date, any payment or advance will have its total amount applied to the principal. Therefore, carry the amount in (8) across to this column.
  10. Subtract the amount in (9) from the amount in this column on the previous row to create the new balance in the account. Copy this amount to the next row in (3).

Calculating a Repayment Schedule

Although the calculations of a repayment schedule are relatively straightforward, the complexity of the repayment schedule sometimes causes grief. When a repayment schedule is required, follow these steps.

  1. Set up the repayment schedule as per the example table.
  2. Record the start date and the opening balance for the loan.
  3. In chronological order, make new row entries in the schedule by filling in the details provided in the question. You require a new row in the table whenever one of the following three events occurs.
    1. A payment or advance is made.
    2. An interest payment date occurs.
    3. The interest rate changes.
  4. Starting with the first row, work left to right across the table, filling in all information. Pay particular attention to the nuances of the “Payment or Advance” and “Principal Amount” columns as discussed previously. Once a row is complete, move to the next row until you fill in the entire table.
  5. Calculate any totals requested such as total interest or total principal paid.

NOTES

  1. For simplicity in writing the numbers into repayment schedules and performing calculations, it is this textbook’s practice to round all interest calculations to two decimals throughout the table. In real-world applications, you must keep track of all decimals in the account at all times.
  2. Because of the size of the repayment schedule and the large amount of information involved in the calculations, the number-one error is what most people call a “silly” error. It means that a wrong date is recorded, a wrong amount is written down, a payment is recorded as an advance or vice versa, or simply the wrong button is pressed on a calculator. Take the time to ensure you read and record the correct numbers and that you pause when performing calculations. For example, advances mean the balance should get bigger, while payments mean the balance should get smaller. Just by thinking for a second about the basic principles of debt you should be able to catch those silly errors.

EXAMPLE

On July 15, 2023, Canadian Footwear took out an operating loan from CIBC for $8,000 at a rate of 5.25% simple interest. The terms of the loan require a fixed payment of $1,500 on the 15th of every month until the loan is repaid. On September 29, 2023, the interest rate on the loan increased to 5.75%. Create a repayment schedule for the loan and calculate the total interest paid.

Solution:

Step 1: The given information is

[latex]\begin{eqnarray*} \mbox{Opening balance on July 15} & = & \$8,000 \\ \\ \mbox{Interest rate on July 15} & = & 5.25\%  \\ \mbox{Interest rate on September 29} & = & 5.75\% \\ \\ \mbox{Payment on 15th of each month} & = & \$1,500 \end{eqnarray*}[/latex]

Step 2:  Set-up the repayment schedule.

Date Balance Before Transaction Annual Interest Rate Number of Days Interest Charged Accrued Interest Payment or Advance Principal Amount Balance After Transaction
July 15 $8,000
Aug 15 $8,000 5.25% 31/3651 $35.672 $35.67 $1,500 $1,464.333 $6,535.674
Sept 15 $6,535.67 5.25% 31/365 $29.14 $29.14 $1,500 $1,470.86 $5,064.81
Sept 29 $5,064.81 5.75% 14/365 $10.20 $10.20 $0 $0 $5,064.81
Oct 15 $5,064.81 5.75% 16/365 $12.77 $22.975 $1,500 $1,477.03 $3,587.88
Nov 15 $3,587.88 5.75% 31/365 $17.52 $17.52 $1,500 $1,482.48 $2,105.30
Dec 15 $2,105.30 5.75% 30/365 $9.95 $9.95 $1,500 $1,490.05 $615.25
Jan 15 $615.25 5.75% 31/365 $3.00 $3.00 $618.256 $615.257 $0

Selection calculations from the table are provided below.

  1. This is the number of days from the date on the previous row to the current row, or July 15 to August 15. Count the first day, but not the last.
  2. [latex]I = P  \times r \times t = 8000 \times 0.0525 \times \frac{31}{365} = \$35.67[/latex]
  3. [latex]1,500.00 − 35.67 = \$1,464.33[/latex]. The accrued interest of $35.67 is now paid and can be crossed out.
  4. [latex]8,000.00 − 1,464.33 = \$6,535.67[/latex]
  5. [latex]10.20 + 12.77 = \$22.97[/latex]
  6. The last payment must clear the balance owing and the accrued interest: [latex]615.25 + 3.00 = \$618.25[/latex].
  7. [latex]618.25 − 3.00 = \$615.25[/latex]

Step 3:  Calculate the total interest paid by adding up the Interest Charged column.

[latex]\begin{eqnarray*} \mbox{Total Interest} & = & 35.67+29.14+10.20+12.77+17.52+9.95+3 \\ & = & \$118.25 \end{eqnarray*}[/latex]

EXAMPLE

Lynne has access to a HELOC that requires only the payment of accrued interest on the first of every month. On March 1, 2023, the opening balance on her HELOC was $15,000. She took advances of $6,000 and $10,000 on March 21, 2023 and May 4, 2023, respectively. She made additional payments of $11,000 and $15,000 on April 15, 2023 and June 17, 2023 respectively. On March 1, 2023, the interest rate on her HELOC was 5%.  On April 26, 2023, the interest rate increased to 5.5%. Construct the repayment schedule from March 1, 2023 to July 1, 2023 and determine the total interest paid from March 1, 2023 to July 1, 2023.

Solution:

Step 1: The given information is

[latex]\begin{eqnarray*} \mbox{Opening balance on March 1} & = & \$15,000 \\ \\ \mbox{Interest rate on March 1} & = & 5\%  \\ \mbox{Interest rate on April 26} & = & 5.5\% \\  \\ \mbox{Advance on March 21} & = & \$6,000 \\ \mbox{Advance on May 4} & = & \$10,000 \\ \\ \mbox{Payment on April 15} & = & \$11,000 \\ \mbox{Payment on June 17} & = & \$15,000\end{eqnarray*}[/latex]

Step 2:  Set-up the repayment schedule.

Date Balance Before Transaction Annual Interest Rate Number of Days Interest Charged Accrued Interest Payment or Advance Principal Amount Balance After Transaction
Mar 1 $15,000
Mar 21 $15,0001 5% 20/3652 $41.103 $41.104 -$6,000 -$6,0005 $21,0006
Apr 1 $21,000 5% 11/365 $31.64 $72.747 $72.748 $09 $21,000
Apr 15 $21,000 5% 14/365 $40.27 $40.27 $11,000 $11,000 $10,000
Apr 26 $10,000 5% 11/365 $15.07 $55.34 $0 $0 $10,000
May 1 $10,000 5.5% 5/365 $7.53 $62.87 $62.87 $0 $10,000
May 4 $10,000 5.5% 3/365 $4.52 $4.52 -$10,000 -$10,000 $20,000
June 1 $20,000 5.5% 28/365 $84.38 $88.90 $88.90 $0 $20,000
June 17 $20,000 5.5% 16/365 $48.22 $48.22 $15,000 $15,000 $5,000
July 1 $5,000 5.5% 14/365 $10.55 $58.77 $58.77 $0 $5,000

Selection calculations from the table are provided below.

  1. This is the balance from the last column in the row above carried forward.
  2. The date interval from the previous row to this row is March 1 to March 21: 20 days.
  3. [latex]I = P \times r \times t = 15,000 \times 0.05 \times \frac{20}{365} = \$41.10[/latex].
  4. The accrued interest from the row above plus (3):  [latex]0 + 41.10 = \$41.10[/latex].
  5. Not an interest payment date, so the full payment is applied to principal: −$6,000
  6. Previous balance in the column above minus the principal portion from (5):  [latex]15,000 − (−6,000) = \$21,000[/latex].
  7. The accrued interest from the row above plus interest from this row:  [latex]41.10 + 31.64 = \$72.74[/latex].
  8. This is an interest payment date. Carry (7) across and cross it out, reducing the accrued interest balance to zero.
  9. This is an interest payment date. Take (8) and subtract (7): [latex]72.74 − 72.74 = \$0[/latex]

Step 3:  Calculate the total interest paid by adding up the Interest Charged column:

[latex]\begin{eqnarray*} \mbox{Total Interest} & = & 41.10+31.64+40.27+15.07+7.53 \\ &  & +4.52+84.38+48.22+10.55 \\ & = & \$283.28 \end{eqnarray*}[/latex]

Exercises

  1. Lacy has took out $40,000 demand loan at 5.25%.  Five months after she took out the loan, the interest rate increased to 6% and twelve months after she took out the loan, the interest rate decreased to 5.7%.  Lacy repaid the loan fifteen months after she took out the loan.  How much interest did Lacy pay on the loan?
    Click to see Answer

     $2845

     

  2. Sam received a $15,000 demand loan at 4.3% on March 20, 2023.  On June 12, 2023 the interest rate changed to 4.7% and on August 19, 2023 the interest rate changed to 3.9%.  Sam repaid the loan on September 7, 2023.  How much interest did Sam pay on the loan?  How much did Sam pay on September 7 to clear the loan?
    Click to see Answer

     $310.23

     

  3. A local business took out a $17,500 operating loan on February 15, 2023 at a rate of 3.75%.  The business made a $3,000 payment on March 29, 2023 and a $4,500 payment on May 4, 2023.  The business repaid the loan on June 28, 2023.  What is the size of the business’s final payment on June 28?
    Click to see Answer

     $10,186.66

     

  4. Mohammad received a operating loan $25,000 operating loan at 4.9%.  Mohammad made payments of $4,000, $300 and $2,000 at six months, ten months and fifteen months after he received the loan.  Mohammad paid off the loan in eighteen months.  What is the size of Mohammad’s final payment?
    Click to see Answer

     $20,353.07

     

  5. A $7,500 demand loan was taken out on March 4, 2023 at a fixed interest rate of 7.72% with fixed monthly payments of $1,200. The first monthly repayment is due April 4, 2023 and the 4th of every month thereafter. Prepare a full repayment schedule for the loan.
    Click to see Answer
    Date Balance Before Transaction Annual Interest Rate Number of Days Interest Charged Accrued Interest Payment or Advance Principal Amount Balance After Transaction
    Mar 5 $7,500
    Apr 4 $7,500 7.72% 31/365 $49.18 $49.18 $1,200 $1,150.82 $6,349.18
    May 4 $6,349.18 7.72% 30/365 $40.29 $40.29 $1,200 $1,159.71 $5,189.47
    June 4 $5,189.47 7.72% 31/365 $34.03 $34.03 $1,200 $1,165.97 $4,023.50
    July 4 $4,023.50 7.72% 30/365 $25.53 $25.53 $1,200 $1,174.47 $2,849.03
    Aug 4 $2,849.03 7.72% 31/365 $18.68 $18.68 $1,200 $1,181.32 $1,667.71
    Sept 4 $1,667.71 7.72% 31/365 $10.93 $10.93 $1,200 $1,189.07 $478.64
    Oct 4 $478.64 7.72% 30/365 $3.04 $3.04 $478.64 $478.64 $0

     

  6. Vertical Adventures has an open line of credit with a zero balance at its credit union using a fixed interest rate of 7.35%. On the last day of every month, the accrued interest must be paid. On July 8 and August 14, the company made advances of $15,000 and $12,000, respectively. On July 30, it made a payment of $10,000. Vertical Adventures will restore its zero balance on August 31. Construct a full repayment schedule from July 8 to August 31.
    Click to see Answer
    Date Balance Before Transaction Annual Interest Rate Number of Days Interest Charged Accrued Interest Payment or Advance Principal Amount Balance After Transaction
    July 8 $15,000
    July 30 $15,000 7.35% 22/365 $66.45 $66.45 $10,000 $9,933.55 $5,066.45
    Aug 14 $5,066.45 7.35% 15/365 $15.30 $15.30 -$12,000 -$12,000 $17,066.45
    Aug 31 $17,066.45 7.35% 17/365 $58.42 $73.72 $17,140.17 $17,066.45 $0

     

  7. Scotiabank approved a $250,000 line of credit for Buhler Industries at 7.5%. It requires only the repayment of accrued interest on the 27th of each month, which is automatically deducted from the chequing account of Buhler Industries. Buhler took out an advance on December 2, 2022 for $200,000.  Buhler made payments of $1,000 on December 27, 2022, $125,000 on January 12, 2023 and $5,000 on January 31, 2023.  On January 4, 2023, the interest rate changed to 8.5%.  Construct a full repayment schedule from December 2, 2022 to January 31, 2023.  Calculate the total interest charged to Buhler Industries from December 2, 2022 to January 31, 2023.
    Click to see Answer
    Date Balance Before Transaction Annual Interest Rate Number of Days Interest Charged Accrued Interest Payment or Advance Principal Amount Balance After Transaction
    Dec 2 $200,000
    Dec 27 $200,000 7.5% 25/365 $1,027.40 $27.40 $1,000 $0 $200,000
    Jan 4 $200,000 7.5% 8/365 $328.77 $356.17 $0 $0 $200,000
    Jan 12 $200,000 8.5% 8/365 $372.60 $728.88 $125,000 $124,271.23 $75,728.77
    Jan 31 $75,728.77 8.5% 19/365 $335.07 $335.07 $5,000 $4,664.93 $71,063.84

    Total Interest=$2063.84

Attribution

“8.5: Application: Loans” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.

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