Mr Koh borrows $950 at a rate of $r\%$ per year compounded quarterly. At the end of 10 years, he has paid $2200. Calculate the value of r. Answer r = ...

1. Set up the compound interest equation for quarterly compounding over 10 years.

There are $10 \times 4 = 40$ quarters.

Quarterly multiplier:
$1+\frac{r/4}{100}=1+\frac{r}{400}$

So
$950\left(1+\frac{r}{400}\right)^{40}=2200.$

2. Isolate the quarterly multiplier.

$\left(1+\frac{r}{400}\right)^{40}=\frac{2200}{950}$

$1+\frac{r}{400}=\left(\frac{2200}{950}\right)^{\frac{1}{40}}$

3. Calculate $r$ using a calculator.

$\frac{r}{400}=\left(\frac{2200}{950}\right)^{\frac{1}{40}}-1$

$r=400\left[\left(\frac{2200}{950}\right)^{\frac{1}{40}}-1\right]$

$r=8.486\ldots$

$r=8.49 \text{ to 3 s.f.}$