The difference between the compound interest (compounding half-yearly) for 1 year and the simple interest for 1 year on a certain sum lent out at the annual rate of 30 percent is Rs. 337.5. What is the sum?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. Rs. 15000.
We know that,
S.I. = (P × R × T)/100
here, S.I. = Simple Interest, P = principal, R = Rate, and T = Time
and, C.I. = P(1 + R/100)T - P
here, C.I.= Compound Interest
⇒ (P(1 + 15/100)2 - P) - (P × 30 × 1)/100 = 337.5
⇒ (P(1 + 0.15)2 - P) - (P × 30 × 1)/100 = 337.5
⇒ (P(1.15)2 - P) - (P × 30 × 1)/100 = 337.5
⇒ (1.3225P - P) - 0.3P = 337.5
⇒ 0.3225P - 0.3P = 337.5
⇒ 0.0225P = 337.5
⇒ P = Rs.15000