1. Sam and Sally (both age 35) plan to retire at age 65. They estimate their ann

Question

1. 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 Social Security. They expect to earn 7% after-taxes both before and after retirement. They also expect inflation to be constant at 4%. They expect to live 30 years after retiring. What amount of money will Sam and Sally need at the beginning of the retirement period to fund an annual income need that increases with inflation? Select the correct answer and show all of your work.

a. $1,003,587

b. $1,117,225

c. $1,327,848

d. $2,943,062

e. $3,319,620

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

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