A scholarship fund makes payments at the end of every six mo

A scholarship fund makes payments at the end of every six months. Each payment in the first year is $500, each payment in the second year is %510, each payment in the third year is $520, and so on. The payments are perpetual. If i=0.075, how much money must be on hand today to fund the scholarship?

Solution

Given i = 0.075 assuming this is per annum basis, For Six months i = 0.075 X 12 / 6 = 0.0375

Consider Six months as a period and i = 0.0375 is for the period.

Observe the payment Structure,

First Year = $ 500

Second Year = $ 510

Third Year = $ 520

There is a growth = 510-500 / 500 X 100

= 10 / 500 X 100

= 2 % i.e $ 10 every year

= 500 / 0.0375 - 0.02

= 500 / 0.0175

= $ 28,571