Question

Avi expects to retire in 12 years. Beginning one month after his retirement he would like to receive $500 per month for 20 years. How much must he deposit into a fund today to be able to do so if the rate of interest on the deposit is 6% compounded monthly?

Answer 1

To calculate the amount Avi must deposit into a fund today, we can use the present value formula for an ordinary annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:

PV = Present Value (amount to be deposited today)

PMT = Payment amount per period ($500 per month)

r = Interest rate per period (6% divided by 12, as it is compounded monthly)

n = Number of periods (20 years multiplied by 12, as it is compounded monthly)

Plugging in the values, we get:

PV = $500 * (1 - (1 + 0.06/12)^(-20*12)) / (0.06/12)

Calculating this equation, we find:

PV ≈ $500 * (1 - (1 + 0.005)^(-240)) / 0.005

PV ≈ $500 * (1 - 1.005^(-240)) / 0.005

PV ≈ $500 * (1 - 0.31336) / 0.005

PV ≈ $500 * 0.68664 / 0.005

PV ≈ $68,664

Therefore, Avi must deposit approximately $68,664 into the fund today in order to receive $500 per month for 20 years, with an interest rate of 6% compounded monthly.

Step-by-step explanation: