Question

In one year your wealthy younger sister will begin depositing $5,000 each year into a savings account for your retirement. The account will compound interest at 5 percent annually and you can't withdraw any money from the account until you retire in 40 years. Which of the following statements is correct?

A. The total amount of interest you will earn will equal $500 ×.05 × 40.

B. The account's value at retirement is given by 5,000/(1.05^60-1)/.005

C. The future value of the account is equal to 500X(1+.05)^40

D. The interest you earn 6 years from now ill equal the interest you earn 10 years from now.

Answer 1

Annual Deposits = $ 5000 with first deposit coming in one year from now (at t=1)

Interest Rate = 5 % and Deposit Tenure = 40 years

Therefore, Total Future Value of Deposits = 5000 x (1.05)^(39) + 5000 x (1.05)^(38) + .....+ 5000 x (1.05) + 5000 = $ 603998.9

Total Interest Earned = Total Future Value - Total Deposits Made = 603998.9 - 5000 x 40 = $ 403998.9  

As is observable, the first three statements are all false and hence only statement (D) is correct.