Question

How do you calculate the average gross replacement rate? Assume from age 18-22 earns $23,400, then...

How do you calculate the average gross replacement rate? Assume from age 18-22 earns $23,400, then from age 23 to 60 earns $100,000 p.a. From this, translate average wealth at retirement to retirement income by computing the consumption the member could achieve if he lives 25 years in retirement and the interest rate is 3% p.a.

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Answer #1

The average gross replacement rate can be calculated using 'annuity formula', that is if a person saves 'x' amount by making monthly saving payments to a retirement portfolio, so that after he retires he can get the wealth at a replacement rate of current monthly earnings (usually salary).

Let us assume at retirement he wants $100,000 p.a post-retirement for 25 years

Present value of annuity= C*[1-(1+i)-n)/i]

Where

C=cash flow=$100,000

i=interest rate=3%

n=payments made=25

Substituting

100,000*[1-(1.03)-25)]/0.03

=$1,741,315 is the present value of annuity to be saved by age of 60 years for hte investor to get a yearly annuity payment of $100,000.

Wealth at retirement=107,237+2,249,273

The present value of retirement wealth=$ 2,356,510

The amount of wealth at retirement considering 3% interest rate is $8,399,819.414.

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