Question

On what sum of money will compound interest (payable annually) for 2 years be the same as simple interest on Rs. 9,430 for 10 years, both at the rate of 5 percent per annum?

Answer 1

P = Rs. 9430

R = 5%

T = 10 years

SI = `[ 9430 xx 5 xx 10 ]/100`

= Rs. 4715

Let sum = X

CI = 4715, T = 2 years, R = 5%

CI = A - P

`4715 = "X"[ 1 + "R"/100 ]^"T" - "X"`

`4715 = "X"[ 1 + 5/100 ]^2 - "X"`

`4715 = "X"|(21/20)^2 - 1|`

`4715 = "X"([ 441 - 400]/400)`

`"X" = [ 4715 xx 400]/41`

Thus, principal from = Rs. 46,000