# Time Value of Money Concepts

After a protracted legal case, Joe won a settlement that will pay him $11,000 each year at the end of the year for the next ten years. If the market interest rates are currently 5%, exactly how much should the court invest today, assuming end of year payments, so there will be nothing left in the account after the final payment is made?

Mary just deposited $33,000 in an account paying 7% interest. She plans to leave the money in this account for eight years. How much will she have in the account at the end of the seventh year?

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 $1500 in a savings account set aside for the furniture. They would like to make three 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 6% interest, how much should the year end payments be?

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#### Solution Preview

1.

Here periodic payments are made at the end of periods. It is a case of ordinary annuity. Amount that court should deposit is equal to the present value of given ordinary annuity.

We know that PV of ordinary annuity=PV=R/i*(1-1/(1+i)^n)

R=Annual payment =$11000

i=Interest rate =5% (assume interest rate remains the same throughout 10 years)

n=Number of annual payments =10

Put values of various parameters

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#### Solution Summary

There are three problems related to time value of money concepts. Solution to first problem describes the methodology to find out present value of given cash flows. Solution to second problem describes the steps to find out the sum of annuity. Solution to third problem explains the steps to find out annual payments to meet a certain financial goal.