A sum of ₹4500 is lent at compound interest. If the rate of interest is 10% per annum (interest is compounded annually), then what will be the amount after 3 years?

Options

A. ₹5989.5
B. ₹5689.5
C. ₹5686.5
D. ₹5889.5

Answer

To find the amount after 3 years when ₹4500 is lent at a compound interest rate of 10% per annum, we can use the formula for compound interest:

**Formula:**
\[ A = P \left(1 + \frac{r}{100}\right)^t \]

Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (initial sum of money)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

**Step 1: Identify the values**
- Principal \( P = ₹4500 \)
- Rate of interest \( r = 10\% \)
- Time \( t = 3 \) years

**Step 2: Substitute the values into the formula**
\[ A = 4500 \left(1 + \frac{10}{100}\right)^3 \]

**Step 3: Simplify the expression inside the parentheses**
\[ A = 4500 \left(1 + 0.10\right)^3 \]
\[ A = 4500 \left(1.10\right)^3 \]

**Step 4: Calculate \( (1.10)^3 \)**
\[ (1.10)^3 = 1.10 \times 1.10 \times 1.10 \]
\[ = 1.331 \] (approximately)

**Step 5: Multiply by the principal**
\[ A = 4500 \times 1.331 \]
\[ A = 5989.5 \]

**Step 6: Final Amount**
The amount after 3 years is approximately ₹5989.50.

### Final Answer:
The amount after 3 years will be ₹5989.50.

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