A married couple desire an annual retirement income of $40,000. They expect to live for 30 years past retirement. Assumi...
A married couple desire an annual retirement income of $40,000. They expect to live for 30 years past retirement. Assuming that the couple could earn a 3% after-tax and after-inflation rate of return on their investments, what amount of accumulated savings and investments would they need?
Homework Answers
Accumulated savings and Investment = Present value of annuity of 40,000 for "n = 30" years at "r = 3%"
The discount rate used for computing the present value must always be after tax and also real rate ( i,e after adjustment of inflation).
Thus using a lower discount rate of 3% ( compared to before tax and nominal rate) requires higher fund need for investment. When we compute before tax rate on such fund and deduct the tax adjustment and inflation we will get 400,000 per year.
Thus, PVIFA = [ 1 - (1+r)-n ] / r
= [ 1 - (1.03)-30 ] / 0.03
= 19.60044135
Accumulated savings and investment = 19.60044135 * 40000
= 784,017.65
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