We have P = Rs 8000,   R = 5% p.a.,      T = 2 years

Calculating Compound Interest

To find the compound interest (CI) on a sum of rupees 8000 for 2 years at an annual interest rate of 5% compounded annually, we can use the formula:

CI = P * (1 + R/100)^T - P

Where:
CI = Compound Interest
P = Principal amount (initial sum)
R = Rate of interest per annum
T = Time period in years

Step 1: Identifying the Variables

In this case, we have:
P = 8000 rupees (the initial sum)
R = 5% (the annual interest rate)
T = 2 years (the time period)

Step 2: Substituting the Values into the Formula

Now, let's substitute the given values into the formula and calculate the compound interest:

CI = 8000 * (1 + 5/100)^2 - 8000
= 8000 * (1 + 0.05)^2 - 8000
= 8000 * (1.05)^2 - 8000
= 8000 * 1.1025 - 8000
= 8820 - 8000
= 820 rupees

Step 3: Interpretation of the Result

Therefore, the compound interest on a sum of rupees 8000 for 2 years at an annual interest rate of 5% compounded annually is 820 rupees. This means that after 2 years, the initial sum of 8000 rupees will have grown to 8820 rupees.

Compound interest is different from simple interest as it takes into account the interest earned on the principal amount as well as the interest accumulated over time. This leads to a higher total interest earned compared to simple interest.

In Summary:
- Principal amount (P) = 8000 rupees
- Annual interest rate (R) = 5%
- Time period (T) = 2 years
- Compound Interest (CI) = 820 rupees

By using the compound interest formula, we have calculated the compound interest to be 820 rupees.