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A man who is going to be living abroad for 2 years wants to buy an ordinary annuity that will provide monthly payments of $750 to his parents at the end of each month while he is gone. The interest rate he can obtain is 6% compounded monthly.
a) Over the 2 years, how much money will his parents receive from their son?
b) What is the amount of the annuity that he must buy now (present value) to generate these payments?

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Answer:

a. $18,000

b. $16,922.18

Explanation:

a. The parents will receive $750 every month for 2 years while the man is away.

That means $750 for 24 months.

Total = 750 * 24

= $18,000

b. Payment is monthly so interest and period have to be converted accordingly.

2 years = 24 months

6% per year = 6/12 = 0.5% a month

Present Value of annuity formula;

PV = Pmt x (1 - (1 / (1 + i)^n)) / i

= 750 * ( 1 - (1 / 1.005^24))/0.005

= 750 * 22.5629

= $16,922.18

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