Question

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

Answer 1

Answer:

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  

Answer 2

Answer:

$1,307

The interest is compounding annually; therefore, it is increasing exponentially.

A = P( 1 + r/n)nt

Repay in 5 years: 5000(1 + 0.08)5 = $7,347

Amount of interest: $7,347 − $5,000 = $2,347

Repay in 3 years: 5000(1 + 0.065)3 = $6040

Amount of interest $6,040 − $5,000 = $1,040

Savings: $2,347 − $1,040 = $1,307