Question

Your cousin Vinny wants to borrow $23750. He’s willing to pay you back over 8 years with simple interest. Your alternative is to invest in the $23750 into an account paying 7.75% compounded monthly.
A) How much interest would you earn in your investment if you deposit $23750 into an investment account for 8 years? Round to nearest cent.
B) What annual interest rate to you charge Vinny in order to make the same amount of interest on his loan as your investment account? Round to nearest hundredth of a percent.

Answer 1

Answer:

A)You will earn $20311.62 as interest  if you deposit $23750 into an investment account for 8 years.

B) The annual interest rate to you charge Vinny in order to make the same amount of interest on his loan as your investment account is 10.69%

Step-by-step explanation:

We are given that Your cousin Vinny wants to borrow $23750. He’s willing to pay you back over 8 years with simple interest.

Your alternative is to invest in the $23750 into an account paying 7.75% compounded monthly.

a)How much interest would you earn in your investment if you deposit $23750 into an investment account for 8 years?

Principal = 23750

Rate of interest = 7.75%

No. of compounds per year = 12

Time = 8 years

Formula : $A=P(1+\frac{r}{n})^{nt}$

Where A is the amount

P is the principal

r = rate of interest

n = No. of compounds

t = time

Substitute the value sin the formula :

$A=23750(1+\frac{7.75}{1200})^{12 \times 8}$

A=44061.6163406

Interest = Amount - Principal

Interest = 44061.6163406-23750

Interest =20311.62

You will earn $20311.62 as interest  if you deposit $23750 into an investment account for 8 years.

B)What annual interest rate to you charge Vinny in order to make the same amount of interest on his loan as your investment account

Principal = 23750

Simple interest =$\frac{P \times T \times R}{100}$

$20311.62=\frac{23750 \times 8 \times R}{100}\\\frac{20311.62 \times 100}{23750 \times 8}=R\\10.69\%=R$

Hence The annual interest rate to you charge Vinny in order to make the same amount of interest on his loan as your investment account is 10.69%