Question

a sum of money is lent out at compound interest for two year at 20% p.a,C.I being reckoned yearly.if The same sum of money Lent out at compound interest at the same rate percent per annum,C.I being reckoned half yearly,it is would have fetched 482 More by way of interest calculate the sum of money Lent out​

Answer 1

Answer:

we can solve this problem either by taking sum of money as x and proceed or use unitary method to get a solution. let us use unitary method

let the sum be Rs 100, r = 20% , n = 2 years

A' = amount (compounded semiannually) and

A = amount (compounded annually)

and A' - A = Rs 482

A' = 100 ( 1 + 20/200)⁴

A' = 100 ( 1 + 1/10)⁴

=> 100(11/10)⁴

=> Rs 146.41

now A = 100 ( 1+ 20/100)²

=> 100 ( 1 + 1/5)²

=> 100 (6/5)²

=> Rs 144

now A' - A = 146.41 - 144 = Rs 2.41 ( for P = Rs 100)

actual P = (difference × 100) ÷ (difference for P = Rs 100)

P = (482 × 100)/2.41

therefore actual P = Rs 20,000