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

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 10 (a total of 10 payments). The inflation rate is 2.41% and you wish to receive $88 in actual (year-10) dollars from the account at the end of year 10. If the market interest rate for the account is 5.5% 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

Real Interest Rate=(1+nominal interest rate)/(1+inflation)-1=1.055/1.0241-1=3.0173%

-A+88/1.030173+88/1.030173^2+88/1.030173^3+88/1.030173^4+88/1.030173^5+88/1.030173^6+88/1.030173^7+88/1.030173^8+88/1.030173^9+88/1.030173^10=0

Hence, A=$749.9955

We need to deposit 749.9955 now to meet our wishes

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