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)

Answer 1

Given that Amber borrows $1,450 from the bank.

She has two options to pay the loan amount. Pay in 3 years or in 2 years.

Calculation of interest for payment in 3 years.

Loan amount P=1450

Interest rate r=5%=0.05

Time t=3 years

Interest is compounded annually so we will use compound interest formula

$A=P(1+r)^t$

Plug the given value

$A=1450*(1+0.05)^3$

$A=1450*(1.05)^3$

$A=1450*1.157625$

A=1678.55625

Interest = A-P=1678.55625-1450= 228.55625

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Calculation of interest for payment in 2 years.

Loan amount P=1450

Interest rate r=3.5%=0.035

Time t=2 years

Interest is compounded annually so we will use compound interest formula

$A=P(1+r)^t$

Plug the given value

$A=1450*(1+0.035)^2$

$A=1450*(1.035)^2$

$A=1450*1.071225$

A=1553.27625

Interest = A-P=1553.27625-1450= 103.27625

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Now we just have to find the difference of interest in both cases

228.55625-103.27625 = 125.28

Hence final answer is approx $125.

Answer 2

The answer is $126 the asked for 20 charaters so