Question

Q. A sum of money is invested at compound
interest for 9 months at 20% per annum,
when the interest is compounded half-
yearly. If the interest were compounded
quarterly, it would have fetched 210 more
than in the previous case. Find the sum.​

Answer 1

Step-by-step explanation:

Answer:

Rs 823

Step-by-step explanation:

Hi,

Let the money invested be 'X'

If compounded half yearly ,time period  9 months = 3/2 half years

Rate of interest r = 20% per annum

So Rate of interest for half year would be = 10% per half year

Compound Interest = X[(1 + 1/10)^(3/2) - 1]

If compounded quarterly, time period 9 months = 3 quarter years

So Rate of interest for quarter year would be = 5% per half year

Compound Interest = X[(1 + 1/20)³ - 1]

Given that X[(1 + 1/10)³ - 1] - X[(1 + 1/20)^(3/2) - 1] = 210

X[(11/10)³ - (21/20)^(3/2)] = 210

X = Rs 823.30

Hence, the sum invested was approximately Rs 823.

Hope, it helps !