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

Every month expenses required after retirement = $1200

As, the expenses amount will be taken out of Interest earned which is Nominal interest rate of 6%.

So, Present value of Investment at retirement to received interest = Monthly Interest amount/Monthly Interest rate

= $1200/(6%/12)

= $1200/0.5%

= $240,000

So, you need to accumulate $ 240,000 at retirement to receive monthly interest as expense amount.

- Calculating the monthly payment you need to make to accumulate $240,000 using Future value of Ordinary annuity formula:-

Where, C= Periodic Payments

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 20 years*12 = 240

Future value = $240,000

240,000 = C*462.0409

C = $ 519.44

So, the large monthly payment you will need to make is $ 519.44

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