Question

Asked Mar 31, 2019

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Your client is currently 19 years old. Your client wishes to retire at age 71. Your client's expected lifetime is 96 years. Your fund generates a return of 4.3%. Your client wants to have a pension benefit of 143,000. calculate the annual contribution your client needs to make.

Step 1

Two assumptions are required to be made because the question is silent about them:

- All cash flows i.e. annual contribution as well as pension benefit withdrawl occur at the end of year.
- Pension benefit of 143,000 is required every year.

Step 2

Your client is currently 19 years old. Your client wishes to retire at age 71. Your client's expected lifetime is 96 years. Your fund generates a return of 4.3%. Your client wants to have a pension benefit of 143,000.

At the time of retirement, i.e. when age is 71 years,

annuity required, A = 143,000

for time period, N = 96 - 71 = 25 years

Interest rate, I = 4.3%

Hence, PV = A / I x [1 - (1 + I)^{-N}] = 143,000 / 4.3% x [1 - (1 + 4.3%)^{-25}] = 2,164,775

Hence, the size of the kitty required at the time of retirement = S = 2,164,775

Step 3

In order to reach to this size of kitty at t = 71 years, let the annual contribution required be an amount "B"

Hence, S = FV of annuity of B (over T = 71 - 19 = 52 years and interest rate, I = 4.3%)

Hence, S = 2,1...

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