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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?
Sum
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Solution
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
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Concept of Compound Interest - Miscellaneous Problem
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