Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.By how much would you reduce the amount you owe in the first year?
A) $2,404.91
B) $2,531.49
C) $2,658.06
D) $2,790.96
E) $2,930.51

Question

Quizplus · Accepted Answer

To calculate the amount of each installment, we can use the formula:
Installment = Loan amount / present value annuity factor
where present value annuity factor can be found from a present value of an ordinary annuity table.

Using this formula, we can calculate that each installment will be $3,548.25.

To find out how much of this installment goes towards reducing the amount owed, we can use the formula for the interest in the first year:
Interest = Loan amount * rate
Interest = $15,000 * 8.5%
Interest = $1,275

Therefore, the amount that goes towards reducing the amount owed in the first year is:
Installment - Interest = $3,548.25 - $1,275
= $2,273.25

To check, we can calculate the remaining amount owed after the first year:
Remaining amount owed = Loan amount - (installment - interest)
Remaining amount owed = $15,000 - ($3,548.25 - $1,275)
Remaining amount owed = $12,726.75

We can repeat this process for each of the remaining years, using the remaining amount owed after each year as the starting loan amount.

Using this method, we find that the amount by which the loan amount is reduced in the first year is closest to $2,531.49 (choice B).

Suppose You Borrowed $15,000 at a Rate of 8