On a certain sum of money lent out at 40% per annum, the difference between the compound interest for 1 year, payable half yearly, simple interest for 1 year is ₹200. The sum is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. ₹5,000
Given that
The interest rate is 40% per annum compounded half yearly
then Rate = 40/2 = 20% p.a.
Time = 1 × 2 = 2 years
Let the sum borrowed be 100 units
Formula used
C.I. = Sum (1 + rate/100)time - Sum
S.I. = (Sum × rate × time)/100
Calculation
C.I. = 100 ( 1 + 20/100)2 - 100 = 100 (6/5)2 - 100
C.I. = 144 - 100 = 44 units
Now, rate = 40% p.a. , time = 1 year
S.I. = (100 × 40 × 1)/100 = 4000/100 = 40 units
According to the question
⇒ 44 units - 40 units = ₹ 200
⇒ 4 units = ₹ 200
⇒ 1 unit = 200/4 = ₹ 50
Hence, the sum borrowed is 100 units = 50 × 100 = ₹ 5000