Solving for Compound Interest from Simple Interest Data

This problem asks us to find the compound interest (CI) given the simple interest (SI) details for the same principal sum, rate, and time period. We need to first find the principal sum using the simple interest information and then use that principal to calculate the compound interest.

Finding the Principal Sum (P)

We are given:

• Simple Interest (SI) = Rs. 1,200
• Rate (R) = 5% per annum
• Time (T) = 3 years

The formula for Simple Interest is:

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

We can rearrange this formula to solve for the Principal (P):

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

Now, let's substitute the given values into the formula:

$P = \frac{1200 \times 100}{5 \times 3}$

$P = \frac{120000}{15}$

$P = 8000$

So, the principal sum of money is Rs. 8,000.

Calculating the Compound Interest (CI)

Now that we have the principal sum, we can calculate the compound interest. We have:

• Principal (P) = Rs. 8,000
• Rate (R) = 5% per annum
• Time (T) = 3 years

The formula for Compound Interest is:

$CI = P \left[ \left(1 + \frac{R}{100}\right)^T - 1 \right]$

Let's plug in the values:

$CI = 8000 \left[ \left(1 + \frac{5}{100}\right)^3 - 1 \right]$

$CI = 8000 \left[ \left(1 + 0.05\right)^3 - 1 \right]$

$CI = 8000 \left[ (1.05)^3 - 1 \right]$

First, calculate $(1.05)^3$: $(1.05)^3 = 1.05 \times 1.05 \times 1.05 = 1.157625$

Now substitute this back into the CI formula:

$CI = 8000 \left[ 1.157625 - 1 \right]$

$CI = 8000 \left[ 0.157625 \right]$

$CI = 1261$

Therefore, the compound interest on the sum of Rs. 8,000 at 5% per annum for 3 years is Rs. 1,261.