Understanding Simple Interest (SI)

Simple Interest is calculated only on the initial principal amount. The formula for Simple Interest is:

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

Where:

• $P$ = Principal amount = ₹12,000
• $T$ = Time period = 2 years
• $R$ = Rate of interest per annum = 8%

Plugging in the values:

$$ SI = \frac{12000 \times 2 \times 8}{100} $$

$$ SI = 120 \times 16 $$

$$ SI = ₹1920 $$

Calculating Compound Interest (CI)

Compound Interest is calculated on the principal amount as well as on the accumulated interest of previous periods. The formula for the Amount (A) after compound interest is applied is:

$$ A = P \left(1 + \frac{R}{100}\right)^T $$

Where:

• $P$ = Principal amount = ₹12,000
• $T$ = Time period = 2 years
• $R$ = Rate of interest per annum = 8%

Calculating the total amount (A):

$$ A = 12000 \left(1 + \frac{8}{100}\right)^2 $$

$$ A = 12000 \left(1 + 0.08\right)^2 $$

$$ A = 12000 \left(1.08\right)^2 $$

$$ A = 12000 \times 1.1664 $$

$$ A = ₹13996.80 $$

Now, calculate the Compound Interest (CI) by subtracting the principal from the total amount:

$$ CI = A - P $$

$$ CI = ₹13996.80 - ₹12000 $$

$$ CI = ₹1996.80 $$

Finding the Difference

The question asks for the difference between the compound interest and the simple interest.

$$ \text{Difference} = CI - SI $$

$$ \text{Difference} = ₹1996.80 - ₹1920 $$

$$ \text{Difference} = ₹76.80 $$

Rounding the difference to the nearest integer, we get ₹77.