Question

Dominique has just turned 58 and she has deposited her annual payment of $15,000 into her retirement account. She made her first such saving deposit into this fund on her 31st birthday. Dominique has also retired and wants to figure out how much money she has in her retirement account for her retired life. You are Dominique's friend who knows finance. How much is Dominique's savings worth today given that the fund has earned an annual return of 3.0%?

Answer 1

FV of annuity = C x [(1+r) ⁿ -1/r]

C = Annual cash deposit = $ 15,000

r = Rate of return = 0.03 p.a.

n = Number of periods = 28 (i.e. from 31 to 58)

FV = $ 15,000 x [(1+0.03) ²⁸ -1/0.03]

     = $ 15,000 x [(1.03) ²⁸ -1/0.03]

     = $ 15,000 x [(2.28792767573726 -1)/0.03]

     = $ 15,000 x (1.28792767573726/0.03)

    = $ 15,000 x 42.9309225245753

    = $ 643,963.83786863 or $ 643,963.84

Dominique’s saving is of $ 643,963.84 today.