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 10 percent is Rs. 305. What is the sum?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. Rs. 122000.
C.I. = P(1 + R/100)T - P and,
S.I. = (P × R × T)/100
here, S.I. = Simple Interest, C.I. = Compound Interest, P = Principal, R = rate, and T = time
⇒ 305 = (P(1 + 5/100)2 - P) - (P × 10 × 1)/100
⇒ 305 = P((1.05)2 - 1) - P/10
⇒ 305 = P(1.1025 - 1) - P/10
⇒ 305 = 0.1025P - P/10
⇒ 3050 = 1.025P - P
⇒ 3050 = P(1.025 - 1)
⇒ 3050 = 0.025P
⇒ P = 3050/0.025
⇒ P = Rs.122000