Question

In how many years will a sum of Rs. 800 at 10% per annum compounded semi-annually become Rs. 926.10 ?
1. \(1 \frac{1}{3}\) years
2. \(1 \frac{1}{2}\) years
3. \(2 \frac{1}{3}\) years
4. \(2 \frac{1}{2}\) years

Answer 1

Correct Answer - Option 2 : \(1 \frac{1}{2}\) years

Given:

Principal = Rs. 800

Rate = 10% per annum compounded semi-annually

Amount = Rs. 926.10

Formula Used:

A = P (1 + R/100)ⁿ

Where, A = Amount, P = Principal, R = Rate, n = time 

Concept Used:

When the rate is compounded semi/half annually then 

The rate becomes R/2 and Time becomes 2n

Calculation:

Let the required time be n

According to the question 

Rate (R) = 10/2% = 5%, Time (n) = 2 × n = 2n

Now, We have to find the amount 

926.10 = 800 (1 + 5/100)²ⁿ

⇒ 926.10/800 = (1 + 5/100)2n

⇒ 1.157625 = (1.05)²ⁿ

⇒ (1.05)³ = (1.05)2n

⇒ 2n = 3

⇒ n = 3/2 = \(1 \frac{1}{2}\)

∴ The required time is \(1 \frac{1}{2}\).