# Time Value of Money

1) 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%, exactly how much should the lottery invest today, assuming end of year payments, so there will be nothing left in the account after the final payment is made?

2) 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?

3) Mary and Joe would like to save up $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?

Show all work for each assignment and explain each step carefully.

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#### Solution Preview

Please see attached file where the answers have been provided.

Note: the abbreviations have the following meanings

FVIF= Future Value Interest Factor

Ordinary Annuity

PVIFA= Present Value Interest Factor for an Annuity

FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations

FVIF( n, r%)= =(1+r%)^n

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%

FVIFA( n, r%)= =[(1+r%)^n -1]/r%

1) 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%, exactly how much should the lottery invest today, assuming end of year payments, so there will be nothing left in the account after the final payment is made?

We have to calculate the Present value of an annuity.

n= 10

r= 12.00%

PVIFA (10 periods, 12.% rate ) = 5.650223

Annuity= $12,000

Therefore, present value= $67,802.68 =12000x5.650223

Answer: The lottery should invest $67,802.68 today

We can see ...

#### Solution Summary

Computes present value of annuity, future value of a lump sum amount and the value of an annuity.