Question

Bill chitty wishes to establish a permanent scholarship paying $2,500 per annum at the end of each year for students wishing to study the change in australian tastes of wines. if interest on investment of this kind is 16% per annum compounded semi-annually what amount needs to be set aside now?

Answer 1

If the interest rate on this type of investment is 16% per year compounded semi-annually, a total of $202500 must be placed aside right now.

The compound interest formula is written as follows:

FV = PV × $({1 + \frac{r}{k} })^{nk}$

FV = face value, PV = price or present value, r = interest rate, n = number of years, and k = number of times compounded in a year.

Each year, $2,500 is paid with an annual interest rate of 16% compounded semi-annually.

Here, PV = 2500, r = 16%, n = 1 and k = 2

FV = 2500 × (1 + (16 ÷ 2))²

FV = 2500 × (1 + 8)²

FV = 2500 × 9²

FV = 2500 × 81

FV = $202500

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