Question

A sum of Rs.8,400 becomes Rs.10,164 in 2 years at a certain rate percentage p.a., interest compounded yearly. What will be the simple interest on the same sum for \(4\frac{3}{5}\) years at the same rate?
1. Rs.3,864
2. Rs.4,454
3. Rs.4,032
4. Rs.4,368

Answer 1

Correct Answer - Option 1 : Rs.3,864

Given:

Principal = Rs. 8,400

Amount = Rs. 10,164

Time = 2 years

Time for SI = \(4\frac{3}{5}\) years = 23/5 years

Formula used:

Amount(A) = P × (1 + r/100)^t

Simple Interest = (P × R × T)/100

Calculation:

∵ Amount(A) = P × (1 + r/100)^t 

⇒ 10,164 = 8400 × (1 + r/100)².

⇒ (1 + r/100)2 = 10,164/8,400

⇒ (1 + r/100)2 = 121/100

⇒ 1 + r/100 = 11/10

⇒ 100 + r = 110

⇒ r = 10

Rate of interest = 10%

SI = (8400 × 10 × 23)/5 × 100

⇒  Rs. 3,864

Alternative Method to find r%:

When time is 2 years;

Amount / Principal = √(10,164/8400) = 11/10

∴ Rate % = [(11 - 10)/10] × 100

⇒ 10%