₹2000 amounts to ₹2226.05 in 2 years on compound interest. What is the rate of interest per annum?

Question

Accepted Answer

The formula for compound interest is:  
$$
A = P \left(1 + \frac{R}{100}\right)^n
$$  
Where:  
- $$ A $$ = Final amount = ₹2226.05  
- $$ P $$ = Principal amount = ₹2000  
- $$ n $$ = Time in years = 2  
- $$ R $$ = Rate of interest per annum (to be calculated).

**Step 1:** Substitute the values into the formula:  
$$
2226.05 = 2000 \left(1 + \frac{R}{100}\right)^2
$$

**Step 2:** Divide both sides by 2000:  
$$
1.113025 = \left(1 + \frac{R}{100}\right)^2
$$

**Step 3:** Take the square root of both sides:  
$$
\sqrt{1.113025} = 1 + \frac{R}{100}
$$  
$$
1.055 = 1 + \frac{R}{100}
$$

**Step 4:** Solve for $$ R $$:  
$$
1.055 - 1 = \frac{R}{100}
$$  
$$
0.055 = \frac{R}{100}
$$  
$$
R = 5.5
$$

Thus, the rate of interest per annum is **5.5%**.

Answer

Answer

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