Write the compound interest formula

The amount $A$ accrued on a principal $P$ at an annual interest rate $R$ compounded annually for $n$ years is given by the formula:

$A = P \left(1 + \frac{R}{100}\right)^n$

Substitute the given values

Substitute $A = 13230$, $P = 12000$, and $n = 2$ into the formula:

$13230 = 12000 \left(1 + \frac{R}{100}\right)^2$

Simplify the ratio

Divide both sides by $12000$ and simplify the fraction by dividing by $30$:

$\frac{13230}{12000} = \frac{441}{400} = \left(1 + \frac{R}{100}\right)^2$

Take the square root on both sides

Since time is $2$ years, taking the square root gives the annual growth multiplier:

$\sqrt{\frac{441}{400}} = 1 + \frac{R}{100} \implies \frac{21}{20} = 1 + \frac{R}{100}$

Solve for the rate of interest R

Subtract $1$ from both sides and solve for $R$:

$\frac{R}{100} = \frac{21}{20} - 1 = \frac{1}{20} \implies R = \frac{100}{20} = 5$