The problem states that a sum of money lent at simple interest becomes $8/5$ of itself in 4 years. We need to find the annual interest rate.

1. Problem Description

The problem states that a sum of money lent at simple interest becomes $8/5$ of itself in 4 years. We need to find the annual interest rate.

2. Solution Steps

Let the principal be $P$.

The amount after 4 years is $A = \frac{8}{5}P$.

The simple interest earned in 4 years is $SI = A - P = \frac{8}{5}P - P = \frac{3}{5}P$.

The formula for simple interest is:

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

where $SI$ is the simple interest, $P$ is the principal, $R$ is the rate of interest per annum, and $T$ is the time in years.

In this case, $SI = \frac{3}{5}P$, $T = 4$ years. We need to find $R$.

$\frac{3}{5}P = \frac{P \times R \times 4}{100}$

Divide both sides by $P$:

$\frac{3}{5} = \frac{4R}{100}$

Multiply both sides by 100:

$\frac{3}{5} \times 100 = 4R$

$60 = 4R$

$R = \frac{60}{4} = 15$

Therefore, the annual interest rate is 15%.

3. Final Answer

15%