Reverse use of the simple interest formula

There are four pronumerals in the formula \(I = PRT\). As with all such formulae, given the values of any three, the value of the fourth can be found.

Example 5

Michael invested $80 000 in a building society that pays 6.5% p.a. simple interest. Over the years the investment has paid him $57 200 in interest. How many years has he had the investment?

Solution

I = 57 200, P = 80 000 and R = 6.5% = 0.065

\begin{align}I &= PRT\\\\ 57\ 200 &= 80\ 000 × 0.065 × T\\\\ 57\ 200 &= 5200 × T\\\\ T &= \dfrac{57\ 200}{5200}\\\\ &= 11\ \text{years}\end{align}