Question

PLEASE HELP!! 50 POINTS!! if you just take the points without actually helping you will be forever cursed within my mind and never forgiven.

Christopher borrows 7,500$ to build a garage. He agrees to pay 475$ a month for 24 months but pays off the loan after 18 months.

Part A: Determine the amount of unearned interest.


Part B: Determine the amount needed to repay the loan using the Rule of 78.


Part C: Show your work to support your answers to Part A and Part B.

Answer 1

To solve the problem, we can use the formula for the future value of an annuity:

FV = PMT * ( (1 + r)^n - 1 ) / r

where:

- PMT is the periodic payment

- r is the periodic interest rate

- n is the number of periods

In this case,

- PMT = $475 (the monthly payment)

- r = the monthly interest rate

- n = 24 (the number of months in the agreement)

We first need to calculate the monthly interest rate. We can find this by dividing the yearly interest rate by 12 months:

r = 18% / 12 months = 0.015

Now we can calculate the future value (FV) of the annuity using the above formula:

FV = $475 * ( (1 + 0.015)^24 - 1 ) / 0.015 = $13,237.19

This is the amount that Christopher would owe after 24 months if he made monthly payments of $475.

However, Christopher pays off the loan after 18 months. To find out how much he owes at this point, we can calculate the future value after 18 months:

FV = $475 * ( (1 + 0.015)^18 - 1 ) / 0.015 = $10,198.66

So, after 18 months, Christopher owes approximately $10,198.66.