The difference between compound and simple interest on a certain sum of money at the interest rate of 20% per annum for years is Rs.6200 when the interest is compounded semi-annually. Find the sum of money.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. Rs. 2,00,000.
We know that,
C.I. = P(1 + R/100)T
S.I. = (P × R × T)/100
where, C.I. = Compound Interest, S.I. = Simple Interest, P = Principle, R = Rate and T = Time
⇒ C.I. - S.I. = (P(1 + R/100)T - P) - (P × R × T)/100
⇒ 6200 = (P(1 + 10/100)3 - P) - (P × 20 × 3)/200
⇒ 6200 = (P(1 + 1/10)3 - P) - 3P/10
⇒ 6200 = (P(11/10)3 - P) - 3P/10
⇒ 6200 = (1331P/1000 - P) - 3P/10
⇒ 6200 = (1331P - 1000P/1000) - 3P/10
⇒ 6200 = 331P/1000 - 3P/10
⇒ 6200 = (331P/1000 - 300P/1000)
⇒ 6200 = 31P/1000
⇒ P = Rs.200000