The problem asks for the time it takes for the simple interest (SI) to equal the principal (P), given information about the SI over 7 years.

Finding the Interest Rate (R)

We are given that the simple interest for 7 years is 56% of the principal.

Mathematically, this is stated as:

$SI = 56\% \times P$

$SI = 0.56 \times P$

The formula for simple interest is:

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

Here, $T = 7$ years.

Substitute the given values into the formula:

$0.56 \times P = \frac{P \times R \times 7}{100}$

We can cancel $P$ from both sides (assuming $P$ is not zero):

$0.56 = \frac{R \times 7}{100}$

Now, solve for the rate $R$:

$R = \frac{0.56 \times 100}{7}$

$R = \frac{56}{7}$

$R = 8\%$

So, the annual interest rate is 8%.

Calculating Time to Equal Principal

Now, we need to find the time (let's call it $T'$) when the simple interest equals the principal ($SI = P$).

Using the simple interest formula again with $SI = P$ and $R = 8\%$:

$P = \frac{P \times 8 \times T'}{100}$

Cancel $P$ from both sides:

$1 = \frac{8 \times T'}{100}$

Solve for $T'$:

$T' = \frac{100}{8}$

$T' = \frac{25}{2}$

$T' = 12.5$ years

Converting Time to Years and Months

$12.5$ years can be expressed as 12 years and 0.5 years.

To convert the fractional part (0.5 years) to months, multiply by 12:

$0.5 \text{ years} \times 12 \text{ months/year} = 6 \text{ months}$

Therefore, the time required is 12 years and 6 months.