Amber borrows $5,000 from the bank. If she repays the loan in 5 years, the annual interest rate is 8%, compounded annually. However, if she can repay the loan in 3 years, the annual rate is 6.5%, compounded annually. How much interest will Amber save by repaying the loan in 3 years? (to the nearest dollar) A) $1,152 B) $1,307 C) $583 D) $971

Option B is correct

Amount amber will save = $1307

Step-by-step explanation:

The formula of the compound interest is

A = P (1 + r/n) ^ (nt)

If she repays a loan in 5 years

P=$5000 (principle amount)

r=8%=0.08 (interest rate)

t=5 (no of years)

n=1 (no of times per year interest is paid)

A=5000 (1+0.08/1) ^ (1 (5))

A=5000 (1.08) ^5

A=5000 (1.4693)

A=$7346.6403

formula for interest amount is

I=A-P

I=$7346.6403-$5000

I=$2346.64

If she repays a loan in 3 years

P=$5000 (principle amount)

r=6.5%=0.065 (interest rate)

t=3 (no of years)

n=1 (no of times per year interest is paid)

A=5000 (1+0.065/1) ^ (1 (3))

A=5000 (1.065) ^3

A=5000 (1.2079)

A=$6039.7481

formula for interest amount is

I=A-P

I=$6039.7481-$5000

I=$1039.7481

then To find the amount of interest that Amber will save by paying in 3 years we will subtract the amount of interest in 5 years with the amount of interest in 3 years

Interest Amount that amber will save = $2346.64 - $1039.7481

=$1306.8918

That will be nearest to $1,307