Question

Amber borrows $1,450 from the bank. If she repays the loan in 3 years, the annual interest rate is 5%, compounded annually. However, if she can repay the loan in 2 years, the annual rate is 3.5%, compounded annually. How much interest will Amber save by repaying the loan in 2 years? (to the nearest dollar) A) $126 B) $205 C) $230 D) $90

Answer 1

$126

The interest is compounded annually; therefore, the increase is exponential.

A = P( 1 + r/n)nt

3 years: $1450(1 + 0.05)3 = $1679

Amount of interest: $1,679 − $1,450 = $229

2 years: $1,450(1 + 0.035)2 = $1553

Amount of interest: $1553 − $1450 = $103

Difference in interest amounts: $229 − $103 = $126

Answer 2

The answer is A) $126