finance monthly payments

Question

You would like to set up an annuity so that, after you retire, you can take out the interest from the maturity value every month to pay living expenses (you predit that you will need $1200 every month). If you start saving 20 years before retirement into an account paying 6% interest, how large of a monthly payment will you need to make?

Answer 1

This question would require you to use two annuity calculations. One, to find the present value of the needed annuity for retirement. Two, to find the payments based on the now future value of the needed annuity for retirement.

Present Value of Retirement

If we assume retirement is in perpetuity.

1200 = PV * (.06/12)

or

PV = 1200 / (.06/12)

PV = 240,000

Payments needed to build annuity

Use the future value of annuity formula. Take the needed amount for retirement and plug it as your future value. Solve for the payments.

240,000 = PMT * (((1 + (.06/12))^(20*12)-1)/(.06/12))

Simplifies to, 240000 = 462.040895x

PMT = ~ 519.4345

or about $520 a month