Question

A man invests ₹10,000 at 10% compound interest compounded annually; what is the total amount after 2 years?

• A. ₹12,000
• B. ₹12,100
• C. ₹11,000
• D. ₹12,200

Hint:

For compound interest questions: \[ A = P \left(1 + \frac{r}{100}\right)^n \] Example shortcut for 2 years:

• After 1 year: \(10000 \times 1.10 = 11000\)
• After 2 years: \(11000 \times 1.10 = 12100\)

Memory trick: \[ \textbf{Compound Interest = Interest on Interest} \]

Answer 1

The Correct Option is B

Concept:
Compound Interest is the interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, where interest is calculated only on the principal, compound interest allows interest to grow faster because interest is added to the principal each period. The formula for compound amount when interest is compounded annually is: \[ A = P \left(1 + \frac{r}{100}\right)^n \] Where:

• \(A\) = Final amount
• \(P\) = Principal (initial investment)
• \(r\) = Rate of interest per year
• \(n\) = Number of years

Step 1: Identify the given values.
\[ P = 10,000 \] \[ r = 10% \] \[ n = 2 \text{ years} \]
Step 2: Substitute the values into the compound interest formula.
\[ A = 10000 \left(1 + \frac{10}{100}\right)^2 \] \[ A = 10000 (1.1)^2 \]
Step 3: Calculate the value.
\[ (1.1)^2 = 1.21 \] \[ A = 10000 \times 1.21 \] \[ A = 12100 \]
Step 4: Final result.
\[ \boxed{₹12,100} \] Thus, the total amount after 2 years is ₹12,100.