Question

Both John and Mary are aged 20 now. John plans to contribute $100 per month in advance into his superannuation fund for 20 years and stop contributing thereafter. Mary plans to start contributiing $200 per month in advance into her superannuation fund at her 40th birthday until she retires. They both plan to retire at age 60. If the annual rate of return is 06.00%, what are the accumulated values of their superannuation accounts at retirement?

Answer 1

Let’s calculate the deposits as two cash flow strings and then accumulated value by adding both.

Computation of Future value of John’s fund:

Formula for FV of ordinary annuity:

FV = P x [(1+r) ⁿ- 1 /r]

FV = Future value of annuity (at 40^th year)

P = Periodic Payment = $ 100

r = Rate per period = 6 % p.a. or 0.06/12 = 0.005 p.m.

n = Numbers of periods = 20 x 12 = 240

FV = $ 100 x [(1+0.005)²⁴⁰ – 1/0.005]

   = $ 100 x [(1.005)²⁴⁰ – 1/0.005]

  = $ 100 x [(3.310204 – 1)/0.005]

  = $ 100 x (2.310204/0.005)

= $ 100 x 462.0409

= $ 46,204.09

FV of this $ 46,204.09 at the time of retirement compounding monthly @ 6 %:

FV = $ 46,204.09 x (1+0.005)^{12 x 20}

     = $ 46,204.09 x (1.005)²⁴⁰

      = $ 46,204.09 x 3.310204

      = $ 152,944.98

John’s fund at the time of retirement = $ 152,944.98

Computation of Future value of Mary’s fund using the same formula with a cash flow of $ 200/m:

FV = $ 200 x [(1+0.005)²⁴⁰ – 1/0.005]

   = $ 200 x [(1.005)²⁴⁰ – 1/0.005]

  = $ 200 x [(3.310204 – 1)/0.005]

  = $ 200 x (2.310204/0.005)

= $ 200 x 462.0409

= $ 92,408.18

Total fund at the time of retirement = $ 152,944.98 + $ 92,408.18

                                                       = $ 245,353.16