\"You want to set up an account that will pay you $A in constant (year-0) dollar
ID: 2790328 • Letter: #
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 4.37% and you wish to receive $107 in actual (year-7) dollars from the account at the end of year 7. If the market interest rate for the account is 4.7% 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
Year 7 107 nominal=107/1.0437^7=79.31476 real
Real Interest Rate=(1+nominal interest rate)/(1+inflation)-1=1.047/1.0437-1=0.3162%
0=-D
+79.31476/1.003162+79.31476/1.003162^2+79.31476/1.003162^3+79.31476/1.003162^4+79.31476/1.003162^5+79.31476/1.003162^6+79.31476/1.003162^7
Hence, D=$548.2472
We need to deposit $548.2472 now to meet our wishes
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