Question

You want to deposit an equal amount of money every year at the end of each of the next 30 years into an account that pays 7.5% annually compounded interest, in order to be able to retire comfortably. During your retirement years, you want to have the ability to withdraw at the end of each of the 15 years, the amount of $32,000. During your retirement years, you will keep your money in an account that earns 3% annually compounded interest. What should be your annual deposits during your working years?

5,894.27

5,273.85

4,836.65

4,422.74

3,694.55

Answer 1

Based on the given data, we need to back-calculate for arriving at the annual deposits:

Step 1: Need to calculate the Value of Deposit total required at the end of Year 30 to make annual payments of $ 32000 for next 15 years; Hence, we need to find the Present Value (PV) at Year 30

Rate : 3% annual compounded; Period (NPER) = 15 years and Payments (PMT) = $ 30000

Using Excel Formula:

PV(RATE,NPER,-PMT,,0) = PV(3%,15,-30000,,0) = $ 382013.92 --> This is the present value as at Year 30;

However, the same should be considered as the required Future Value by making annual deposits for next 30 years from date at 7.5% annual compounding.

Rate : 7.5% annual compounded; Period (NPER) = 30 years and Future Value (FV) = $ 382013.92

Using Excel Formula:

PMT(RATE,NPER,PV,-FV,0) = PMT(7.5%,30,0,-382013.92,0) = $ 3694.55 --> Answer: This is the annual deposits required;