You want to set up an account that will pay you $A in constant (year-0) dollars

Question

You want to set up an account that will pay you $A in constant (year-0) dollars in each year from the end of year 1 through the end of year 7 (a total of 7 payments). The inflation rate is 3.26% and you wish to receive $130 in actual (year-7) dollars from the account at the end of year 7. If the market interest rate for the account is 4.3% compounded annually, how much to the nearest dollar do you need to deposit now to meet your wishes? You will not make any other deposits after the initial deposit. (HINT : you will need to calculate the inflation-free interest rate to relate $A to the initial deposit.)

Explanation / Answer

First, we need to find out the actual inflation-free interest rate which we would be able to earn and reinvest on our annual savings.

Since, Return = 4.3% and Inflation is 3.26%

The actual inflation-free interest is 1.043/1.0326 - 1 = 1.007%

Now, to be able to accumulate $130 by the end of 7th year, we need to find $A of annual contribution which will earn an interest-free rate of 1.007% and be therefore able to accumulate the required amount.

As it turns out, this is a simple annuity calculation to find $A and can be solved with the following parameters:

Annuity - $A

Interest Rate - 1.007%

Period of Investment - 7 years

Future Value - $130

Solving through a financial calculator or excel, we can find out that $A = $18 appx

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