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 40 percent is Rs. 360. What is the sum?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. Rs. 9000.
C.I. = P(1 + R/100)T - P
here, C.I. = Compound Interest, P = Principal, R = Rate, T = Time
C.I. = P(1 + 20/100)2 - P
S.I. = (P × R × T)/100
here, S.I. = Simple Interest, P = Principal, R = Rate, and T = Time
S.I. = (P × 40 × 1)/100
now, the difference is Rs.360
⇒ P(1 + 20/100)2 - P - ((P × 40 × 1)/100) = 360
⇒ P((1 + 0.2)2 - 1) - (P × 0.4) = 360
⇒ P((1.2)2 - 1) - 0.4P = 360
⇒ P(1.44 - 1 - 0.4) = 360
⇒ P × 0.04 = 360
⇒ P = 360/0.04 = Rs.9000