Question

You have just deposited $10,500 into an account that promises to pay you an annual interest rate of 6.4 percent each year for the next 5 years. You will leave the money invested in the account and 15 years from today, you need to have $29,750 in the account. What annual interest rate must you earn over the last 10 years to accomplish this goal?

Answer 1

Answer:

7.59%

Explanation:

Calculation for What annual interest rate must you earn over the last 10 years to accomplish this goal

Future value required=[Amount of deposit*(1+6.4%)^5]*(1+I)^10

$29,750=[$10,500*(1+6.4%)^5]*(1+I)^10

$29,750=[$10,500*(1+0.064)^5]*(1+I)^10

$29,750=[$10,500*(1.064)^5]*(1+I)^10

$29,750=[$14,318.497198]*(1+I)^10

(1+I)^10=[$29,750/$14,318.497198]

(1+I)^10=2.077732013

(1+I)=2.077732013^(1/10)

(1+I)=1.07586791

Hence, annual interest rate will be:

Interest rate, I=(1.07586791-1)*100

Interest rate=0.07586791*100

Interest rate=7.586791%

Interest rate=7.59% (Approximately)

Therefore the annual interest rate that you must earn over the last 10 years to accomplish this goal is 7.59%