Sam and sally (both age 35) plan to retire at age 65. they estimate their annual

Question

Sam and sally (both age 35) plan to retire at age 65. they estimate their annual income need in retirement will be $50,000 in "today's dollars". they expect to receive $30,000 (in "today's dollars") annually from society security. they expect to earn 7% after-taxes both before and after retirement. $1,003,587 $1,117,225 middot $1,327,848 $2,943,062 $3,319,620 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? (Show your steps in calculations to support your answer) They are okay. The $300,000 will exceed their needs by more than $10,000 They are deficient The $300,000 will be underfunded by almost $27,000 They need to increase their preretirement investment return rate from 7% to 7.12% to meet their goal.

Explanation / Answer

Amount Required by Sam and Sally at retirement = $50000 - 30000 = $20000 in today's term Period remaining for retirement = 30 years Value of $20000 at retirement = 20000 * (1+ 0.04)^30 = 64867.95 This amount will increase by 4% 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 at retirement = [64867.95 / (0.07 - 0.04)] * [1 - (1.04/1.07)^30] = $2162265 * 0.573924 = $1240976 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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