22-year-old engineering graduate wants to accumulate $2,000,000 to be available

Question

22-year-old engineering graduate wants to accumulate $2,000,000 to be available when she retires 40 years from today. She investigates several investment options and decides to invest in a stock market index fund after discovering that the long-term average return for the stock market is 10.4 percent per year. Since this will be a taxsheltered account, she plans to ignore the impact of taxes. If she makes the first of the 40 deposits starting today rather than 1 year from today, what is the dollar amount of the required deposits?

Explanation / Answer

FV of an annuity due = $2,000,000

let annual saving be A

FV of an annuity = (1+r)*A*[(1+r)^n-1]/r

where r is the rate of interest or return = 10.4%

n is no oof years = 40

equation that we have to solved

2000000 = 1.104*A*(1.104^40-1)/.104

2000000 = 1.104*A*493.5718

A = 2000000/(1.104*493.5718) = $3670.37

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