PROBLEMS – Show your work! For time value of money problems, show your inputs, a

Question

PROBLEMS – Show your work! For time value of money problems, show your inputs, and tell me what you use for the calculations! No work and its wrong = 0 points!

(8 points) A friend wants to retire in 30 years when he is 65. At age 35, he can invest $300/month that earns 6% each year. But he is thinking of waiting 15 years when he is age 50, and then investing $900/month to catch up, earning the same 6% per year. He feels that by investing three times as much for half as many years (15 instead of 30 years) he will have more. What is the future value of each of these options at age 65, and under which scenario would he accumulate more money? Scenario A: $ , Scenario B: $ , Best:

Explanation / Answer

Situation 1.

Formula for future value of Annuity :

FV= A [ (1+k)n-1/k]

FV = Future annuity value

A = periodical (monthly) investment =300

K=interest rate=6%=0.5% per month

N=periods=30 years=360 month

FV = 300[(1.005)360-1]/0.005=300[6.023-1]/0.005=301,380

So the future value of the investment =$301,380

Situation 2.

A = periodical (monthly) investment =900

K=interest rate=6%=0.5% per month

N=periods=15 years=180month

FV= 900[(1.005)180-1]/0.005=900(2.454-1)/0.005=261,720

So Future value of investment under second option is $261,720

So under scenario A. he will accumulate more money.

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