On 1st January 2018, Mrs Yeo invests $15000 in an account which pays at a rate of compound interest of $R$% per year. On 1st January 2021, she earned a total interest of $988.45. Find the value of $R$.

1. Find the final amount after 3 years and set up the compound interest equation.

From 1st January 2018 to 1st January 2021 is $3$ years.

Total amount after 3 years
$=15000+988.45=15988.45$

Using compound interest,
$15000\left(1+\frac{R}{100}\right)^3=15988.45$

2. Solve for the annual interest rate.

$\left(1+\frac{R}{100}\right)^3=\frac{15988.45}{15000}$

$1+\frac{R}{100}=\sqrt[3]{\frac{15988.45}{15000}}$

$\frac{R}{100}=\sqrt[3]{\frac{15988.45}{15000}}-1$

$R=100\left(\sqrt[3]{\frac{15988.45}{15000}}-1\right)$

$R=2.15$