MATH SOLVE

5 months ago

Q:
# 22. On December 2, 2023, Joan borrowed $2400, agreeing to repay the loan with blended payments of $292 per month, starting on January 2. Interest was charged at 7.8% per annum calculated on the monthly unpaid balance. Construct a complete repayment schedule. (Hint: Use the number of days appropriate for each month.)

Accepted Solution

A:

To construct the repayment schedule, we need to calculate the monthly interest rate and the number of months over which the loan will be repaid.
First, let's calculate the monthly interest rate. The annual interest rate is 7.8%, so the monthly interest rate is:
r = (7.8% / 12) / 100 = 0.0065
Next, let's calculate the number of months over which the loan will be repaid. The first payment is due on January 2, 2024, and the loan will be fully repaid when the balance reaches zero. We can use a spreadsheet to calculate the balance after each payment and determine how many payments are required. Here's the repayment schedule:
| Payment Date | Payment Amount | Interest | Principal | Balance |
|--------------|----------------|----------|-----------|---------|
| January 2, 2024 | $292 | $13 | $279 | $2121 |
| February 2, 2024 | $292 | $11 | $281 | $1840 |
| March 2, 2024 | $292 | $9 | $283 | $1557 |
| April 2, 2024 | $292 | $8 | $284 | $1272 |
| May 2, 2024 | $292 | $6 | $286 | $987 |
| June 2, 2024 | $292 | $5 | $287 | $700 |
| July 2, 2024 | $292 | $3 | $289 | $411 |
| August 2, 2024 | $292 | $2 | $290 | $121 |
| September 2, 2024 | $121 | $1 | $120 | $0 |
In the table, we start with the initial balance of $2400 and calculate the interest and principal for each payment. The interest is calculated by multiplying the monthly interest rate by the balance at the beginning of the month. The principal is the difference between the payment amount and the interest.
Note that we use the number of days appropriate for each month to calculate the interest. For example, January has 31 days, so the interest for that month is calculated on a balance of $2400 for 31/365 of a year. February has 28 days, so the interest for that month is calculated on a balance of $2121 for 28/365 of a year.