A sum of money becomes four times in $20$ years at simple interest. Find the rate of interest.

Let the principal amount be $P$.
The amount becomes four times in $20$ years, so the final amount $A=4P$.
The simple interest ($SI$) earned is:

$$SI=A-P=4P-P=3P$$

The formula for simple interest is:

$$SI=\frac{P\times R\times T}{100}$$

Given time $T=20\text{years}$. Substituting the values into the formula:

$$3P=\frac{P\times R\times 20}{100}$$

$$3=\frac{R\times 20}{100}$$

$$3=\frac{R}{5}$$

$$R=3\times 5=15\%$$

Therefore, the rate of interest is $15\%$ per annum.