Question

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

Answer 1

Answer: $2,531.49

Step-by-step explanation:

Payments are equal over the 5 years making this an Annuity.

The $15,000 would be the present value of the Annuity.

PV of Annuity = Annuity ( 1 - (( 1 + r) ^-n) / r)

15,000 = A ( 1 - (( 1 + 0.085) ^ -5)/0.085)

15,000 = A * 3.940642

A = 15,000/3.940642

A = $3,806.49

Mortgage Payment Yearly is $3,806.49

Seeing as this is loan repayment, some part of the payment goes towards interest payment and the rest goes towards the repayment of the loan.

The interest is,

= 0.085 * 15,000

= $1,275

The rest goes towards repayment,

= 3,806.49 - 1,275

= $2,531.49

Answer 2

$2,531.49

Step-by-step explanation:

To find the how much would you reduce the amount you owe in the first year, we have to determine the amount of yearly payments.

The formula for finding this is :

A = FV/ annuity factor

Annuity factor = {[(1+r) ^N ] - 1} / r

A = yearly payments

FV = Future value = $15,000

R = interest rate =8.5%

N = number of years = 5

Annuity factor = [(1.085)^5 - 1 ] / 0.085 = 5.925373

= $15,000 / 5.925373 = $2,531.49

I hope my answer helps you