You are saving for retirement. You want to have $800,000 in current purchasing p

Question

You are saving for retirement. You want to have $800,000 in current purchasing power at the end of exactly 40 years. There is no money in the account now. All payments into your fund are at the end of the year and your first payment is exactly one year from now. There are 40 payments. The interest rate is 7% per year and the expected inflation rate is 3% per year.

A.) If each payment into the fund is equal in actual dollars, how much should be deposited each year?

B.) if your salary growth is exactly 3% (the rate of inflation) per year and you wish to increase your annual payment into the fund at that rate, how much should the first payment (one year from now be) in actual dollars.

Please do out using excel and show intermediate steps/formulas. Thanks.

Explanation / Answer

A)Real rate of return= 7%-3%= 4%

Let amount deposited each year =x

Present value of retirement amount = 800000/(1+4%)^40=166631.2

Present value of deposited amount =166631.2

166631.2 = x/1.04^1 + x/1.04^2 + x/1.04^3.......x/1.04^40

Using NPV fuction in excel

amount deposited each year, x=$8418.79

B)

Deposit increases by 3%

166631.2 = x/1.04^1 + x*1.03/1.04^2 + x*1.03^2/1.04^3.......x*1.03^39/1.04^40

depost amount, x= $5198.24

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