The difference between the compound interest (compounding annually) and simple interest on a sum at the rate of 30 percent per annum for 2 years is Rs. 5400. What is the sum?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 3 i.e. Rs. 60000.
Where:
P = Principal
R = Rate of interest (30% per annum)
T = Time period (2 years)
S.I. = (P × R × T)/100
⇒ S.I. = (P × 30 × 2)/100 = 60P/100 = 0.6P
⇒ C.I. = P((1 + R/100)T − 1)
⇒ C.I. = P((1 + 30/100)2 − 1) = P((1.30)2 − 1)
⇒ C.I. = P(1.69 − 1) = P × 0.69
⇒ C.I. − S.I. = 5400
⇒ 0.69P − 0.6P =5400
⇒ 0.09P = 5400
⇒ P = 5400/0.09 = 60000
The sum (principal) is Rs. 60,000.