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

Monthly interest rate = 6%/12 = 0.005

The maturity value should be = Interest/Monthly interest rate

The maturity value should be = 1,200/0.005

The maturity value should be = 240,000

Now, let's find the monthly payments to have the maturity value = $240,000

$FV = \frac{PMT}{r} * \left [ (1+ r )^{n} - 1 \right ]$

$240,000 = \frac{PMT}{0.005} * \left [ (1+ 0.005 )^{240} - 1 \right ]$

240,000 = PMT * 2.3102044758 0.005

240.000 = PMT * 462.04089516

$PMT = \frac{240,000}{462.04089516}$

We will need to make a monthly payment of $519.4345403493

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