Purchase Solution

# Lottery Jackpot and Market Interest Rates

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A) 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?

b) 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?

c) 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?

##### Solution Summary

This solution contains step-by-step calculations to determine the present value of an annuity, future value of a one time deposit and the present value of furniture and savings. All workings are shown with brief explanations.

##### Solution Preview

a) Here we need to calculate the present value of an annuity. We have following things
Annual payment C=12000
Interest rate r=12%
Time duration for the annuity n=10 years
The formula for PV of annuity is
PV=C/r(1-1/(1+r)^n)
=12000/12%*(1-1/(1+12%)^10)=67802.68

b) Here we ...

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