Question

Reed Smith is saving for his eventual retirement. He plans to make 18 contributions to his retirement account at the beginning of each of the next 18 years. The first contribution will be made right now (today, t=0) and the final contribution will be made 17 years from today (i.e., at t=17). The retirement account will earn a return of 10%/ year. If each of Mr. Smith’s contributions is $3000, how much will be in his retirement account 17 years from now? Notice that this question asks for a value at t=17, i.e., at the same time as the final contribution. [Suggestion: Draw a timeline and also refer to the Lesson‐2 handout titled “One Overarching Annuity Example”.]

Answer 1

(1+i) -1 (1 FVAnnuity Due = C

FVAnnuity Due = c*(((1+ i)^n - 1)/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

FV= 3000*(((1+ 10/100)^17-1)/(10/100))*(1+10/100)

FV = 133797.52

Total amount = FV+last deposit = 133797.52+3000= 136797.52