I have a question about nest eggs

Question

Hi can anyone help me answer this question? I am stumped.

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $5000 per month. You have access to an account that pays an APR of 6.0% compounded monthly. This requires a nest egg of $776,034.32.

What monthly deposits are required to achieve the desired monthly yield at retirement?

Answer 1

ok there are 40*12 = 480 months between now and retirement The monthly interest rate is 6%/12 = .5%. The present value of the nest egg is (1/(1.005))^480 times 776,034.32=70822.50. So we want to know what stream of monthly deposit made for 480 months has a present value of 78,822.5

That payment or deposit is Given by i*PV/(1-(1/1+i))^t) = .005*70,822.5/(1-.09126 ) = 433.69 per month.

Please don't hesitate to reach out. I know this stuff cold. After being a professor of economics I spent more than a few years on Wall Street and ran many training sessions on valuing cash flows.

Best,

Lenny