At what rate (in percentage) per year will a sum of money double itself in 16 years on simple interest?

The correct answer is 6.25.

Step-by-Step Explanation:

Step 1: Understand the given information

Let the principal sum of money be P.

According to the problem, the sum doubles itself in 16 years. Therefore, the total amount (A) becomes 2P.

Time period (T) = 16 years.

Step 2: Calculate the Simple Interest

Simple Interest (SI) is given by the difference between the total amount and the principal sum:

$SI=A-P$

$SI=2P-P=P$

Step 3: Apply the Simple Interest formula to find the Rate of Interest

The formula for Simple Interest is:

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

Substitute the values of SI and T into the formula:

$P=\frac{P\times R\times 16}{100}$

Step 4: Solve for the Rate (R)

Divide both sides by P:

$1=\frac{16R}{100}$

Rearrange the terms to find R:

$R=\frac{100}{16}$

$R=6.25\%$

Hence, the rate of interest per year is 6.25%.