Question

You have inherited some money and you want to set some of that money aside for ten years. After ten years, you would like to receive $7600.00 at the end of each 6 months for nine years. If the interest is 6.5% compounded semi-annually, how much of your inheritance must you set aside?

Answer 1

For the time being, please shift yourself to the end of ten years. At this point,

you would like to receive $7600.00 at the end of each 6 months for nine years.

Hence, the period here is 6 months (semi annual, half year)

n = 2 x 9 = 18; A = 7,600; r = 6.5%/2 = 3.25%

Hence, the size of the kitty required at the end of 10 years = PV of annuity = A/r x [1 - (1 + r)-n] = 7,600 / 3.25% x [1 - (1 + 3.25%)-18] = $ 102,351.18

Now come back to t = 0 i.e current time.

The money you want to set aside today to get a kitty of 102,351.18 in 10 years from now

= FV / (1 + r)m

= 102,351.18 / (1 + 3.25%)(2 x 10)

= $  53,987.31

(Please do round it off as per your requirement)