Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest - OCR - GCSE Maths - Question 15 - 2018 - Paper 1

To isolate $\left(1 + \frac{r}{100}\right)^2$, divide both sides by 1200:

$\left(1 + \frac{r}{100}\right)^2 = \frac{1379.02}{1200}$

Calculating the right-hand side gives:

$\left(1 + \frac{r}{100}\right)^2 \approx 1.149185$

Now take the square root of both sides:

$1 + \frac{r}{100} = \sqrt{1.149185}$

Calculating this gives:

$1 + \frac{r}{100} \approx 1.073$

Next, subtract 1 from both sides:

$\frac{r}{100} \approx 0.073$

Then, multiply both sides by 100 to find $r$:

$r \approx 7.3$

Thus, the annual interest rate $r$ is approximately 7.3%.