Find the amount of Rs 1000 after 4 years at the rate of 10% per annum compounded annually.

Options

A. 1464.1
B. 1444.2
C. 1452.2
D. 1425.2

Answer

To find the amount of Rs 1000 after 4 years at the rate of 10% per annum compounded annually, we can use the formula for compound interest:

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

Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (the initial amount of money).
- \( r \) = annual interest rate (in percentage).
- \( n \) = number of years the money is invested or borrowed.

**Step 1: Identify the values**
- Principal (P) = Rs 1000
- Rate of interest (r) = 10%
- Time (n) = 4 years

**Step 2: Substitute the values into the formula**
\[ A = 1000 \left(1 + \frac{10}{100}\right)^4 \]

**Step 3: Simplify the expression inside the parentheses**
\[ A = 1000 \left(1 + 0.10\right)^4 \]
\[ A = 1000 \left(1.10\right)^4 \]

**Step 4: Calculate \( (1.10)^4 \)**
To calculate \( (1.10)^4 \):
\[ (1.10)^4 = 1.10 \times 1.10 \times 1.10 \times 1.10 \]
Calculating step by step:
- \( 1.10 \times 1.10 = 1.21 \)
- \( 1.21 \times 1.10 = 1.331 \)
- \( 1.331 \times 1.10 = 1.4641 \)

So, \( (1.10)^4 = 1.4641 \).

**Step 5: Substitute back to find A**
\[ A = 1000 \times 1.4641 \]
\[ A = 1464.1 \]

**Final Answer:**
The amount after 4 years is Rs 1464.1.

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