Question

A. If you will be making equal deposits into a retirement account for 20 years (with each payment at the end of the year), how much must you deposit each year if the account earns 8% compounded annually and you wish the account to grow to $5,000,000 after 40 years (in time 40)?

b. How does your answer to part (a) change if the account pays interest compounded monthly at an annual rate of 8%?

Answer 1

A) we can use the future value of an annuity formula:

future value = annual contribution x FV annuity factor

• future value = $5,000,000
• FV annuity factor, 8%, 40 periods = 259.05652

annual contribution = $5,000,000 / 259.05652 = $19,300.81

B) we need to calculate the effective annual interest rate:

= (1 + 0.08/12)¹² - 1 = 8.3%

future value = annual contribution x FV annuity factor

• future value = $5,000,000
• FV annuity factor, 8.3%, 40 periods = 280.40756

annual contribution = $5,000,000 / 280.40756 = $17,831.19

your annual contribution will decrease by $1,469.62