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?
$2,404.91


$2,531.49


$2,658.06


$2,790.96


$2,930.51

Answer 1

Answer:

The amount that would be reduce for the first year is $2,531.49

Explanation:

Hi, first we have to find the amount of the equal installments to be paid for the next 5 years, for that, we need to solve for "A" the following equation.

$PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

Where:

Present Value = the borrowed amount

A = equal installments

r = rate of the loan

n = number of periodic and equal installments

Everything should look like this.

$15,000=\frac{A((1+0.085)^{5}-1) }{0.085(1+0.085)^{5} }$

$15,000=A(3.940642079)$

Therefore, A= $3,806.49

Now, in order to find the amount that would be reduced in the first year, we have to use the following formula.

$AMT(reduced)=Payment-Interest$

So, it should look like this.

$AMT(reduced)=3,806.49-15,000*0.085$

$AMT(reduced)=3,806.49-1,275=2,531.49$

Best of luck.