A sum amounts to Rs. 6,050 in 2 years and to Rs. 6,655 in 3 years at a certain rate percentage p.a. when the interest is compounded yearly. What is the simple interest on a sum of Rs. 6,000 at the same rate for 5\(\frac{3}{4}\) years?
1. Rs. 3,450
2. Rs. 3,150
3. Rs. 3,300
4. Rs. 3,200
1. Rs. 3,450
2. Rs. 3,150
3. Rs. 3,300
4. Rs. 3,200
Correct Answer – Option 1 : Rs. 3,450
Given:
A sum amounts to Rs. 6,050 in 2 years and to Rs. 6,655 in 3 years at a certain rate percentage p.a. when the interest is compounded yearly.
Formula:
Let P = Principal, R = rate of interest and N = time period
Simple interest = PNR/100
Compound interest = P(1 + R/100)n – P
Calculation:
Accordingly,
6050 = P(1 + R/100)2
And, 6655 = P(1 + R/100)3
Dividing,
(1 + R/100) = 6655/6050
⇒ R/100 = 6655/6050 – 1
⇒ R/100 = 605/6050
⇒ R = 10%
Simple interest on a sum of Rs. 6,000 at the same rate for 5\(\frac{3}{4}\) years = 6000 × 10/100 × 23/4
⇒ Rs.3450
∴ Required simple interest is Rs. 3450