Question

If Sam deposits $723 each month to his retirement account at a fixed interest rate of 4.12%, how long will it take his funds to reach $187,980?

A. 22 years and 5 months

B. 20 years and 2 months

C. 15 years and 6 months

D. 10 years and 2 months

Answer 1

Required number of periods can be computed using formula for FV of annuity as:

FV = P x [(1+r) n -1/r]

P = Periodic cash deposit = $ 723

r = Rate of interest = 4.12 % p.a. or 0.0412/12 = 0.003433333 p.m.

n = Number of periods

$ 187,980 = $ 723 x [(1 + 0.003433333) n -1 /0.003433333]

$ 187,980 = $ 723 x [(1.003433333) n-1/0.003433333]

(1.003433333) n-1/0.003433333 = $ 187,980/ $ 723

(1.003433333) n-1/0.003433333 = 260

(1.003433333) n – 1 = 260 x 0.003433333 = 0.89266658

(1.003433333) n = 1 + 0.89266658

(1.003433333) n = 1.89266658

Taking log of both sides we get,

n x log 1.003433333 = log 1.89266658

n x 0.0014885237373 = 0.27707411358

n = 0.27707411358/0.0014885237373 = 186.140204980929 periods or months

                                                              = 15 years and 6 months

Sam’s fund will need 15 years and 6 months to reach to $ 187,980.

Hence option “C. 15 years and 6 months” is correct answer.