2. Bob and Mary expect to have $300,000 in retirement funds when they retire in
ID: 2720457 • Letter: 2
Question
2. Bob and Mary expect to have $300,000 in retirement funds when they retire in 15 years (assuming a 7% investment return rate on current assets). When they retire, they expect to need $22,000 annually which will increase with inflation (3%). They can make 8.5% after-tax return on their money. They expect their joint life expectancy to be 21 years after retirement. What would you tell them? Select the correct answer and show all of your work.
a. They are okay. The $300,000 will exceed their needs by more than $10,000
b. They are deficient. The $300,000 will be underfunded by almost $27,000
c. They need to increase their preretirement investment return rate from 7% to 7.12% to meet their goal
Explanation / Answer
Amount Required by Bob and Mary at retirement = $22000 This amount will increase by 3% every year due to inflation This is a classic case of growing annuity. Present Value of Growing Annunity = [P/ (r-g)] * [ 1 - {(1+g)/(1+r)}^n where, P is the first installment r is the rate of return g is the growth rate n is the number of years Present Value = [22000 / (0.085 - 0.03)] * [1 - (1.03/1.085)^21] = $440000 * 0.664605 = $265841.8 Hence, the correct answer is Option A - They are okay. The $300,000 will exceed their needs by more than $10,000
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