Time Value of Money

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A.Q. Joe won a lottery jackpot that will pay him $12,000 each year for the next ten years. If the market interest rates are currently 12%, how much does the lottery have to invest today to pay out this prize to Joe over the next ten years?

A.
If prize = (principal) x (rate) x (time)
prize = (12,000) x (0.12) x (10)
prize = (12,000) x (1.2)
prize = $144,000 total invested by the lottery to pay our winnings of 12,000 for the next ten years.

B.Q. Mary Just deposited $33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in the account at the end of the seventh year?

A.
Traditional method of finding the Future Value:

FV end of year 1 = $33,000+0.10($33,000) = $36,300
FV end of year 2 = $33,000+0.10($36,300) = $39,930
FV end of year 3 = $33,000+0.10($39,930) = $43,923
FV end of year 4 = $33,000+0.10($43,923) = $48,315.30
FV end of year 5 = $33,000+0.10($48,315.30) = $53,146.83
FV end of year 6 = $33,000+0.10($53,146.83) = $58,461.513
FV end of year 7 = $33,000+0.10($58,461.513) = $64,307.6643

or using the FV formula to find the Future Value:

FV=PV(1.0+i)n
FV=$33,000(1.0 + 0.10)7 = $33,000(1.10)7 = $33,000(1.9487171) = $64,307.6643

C.Q. Mary and Joe would like to save up to $10,000 by the end of three years from now to buy new furniture for their home. They currently have $2500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 8% interest, how much should the year end payments be?

A.
Current savings alone with .08% interest after three years would equal $3149.28, a $6850.72 difference in what is needed to bring Mary and Joes savings to $10,000.

FV(1.0+i)n
FV =$2500(1.0+.08)3 = $2500(1.08)3 = $2500(1.259712) = $3149.28

Formula: PV = [1.0 – 1.0 / (1.0 + i)n] x A /...
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