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If the rate of compound interest for the...

If the rate of compound interest for the first year be 3%, for the second year be 2% and for the third year be 1% then find the sum of the money, the amount of which of 3 years is Rs. 15916.59.

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Let the sum of money be Rs. `x`
`:.` At the rate of 3% interest per annum, the amount of Rs.x after first year.
`Rs. x xx (1+3/100)=Rs. (103x)/100`
`:.` for the second year the principal `=Rs. (103x)/100`.
Again at the rate of 2% compound interest per annum,
the amount of Rs. `(103x)/100` for 1 year `=Rs. (103x)/100(1+2/100)=Rs. (103x)/100xx102/100`

`:.` For the third year the principal `=Rs. (103x)/100xx102/100`
At last at the rate of 1% compound interest per annum.
the amount of `Rs. (103x)/100xx102/100` for 1 year
`=Rs. (103x)/100xx102/100xx(1+1/100)`
`=Rs. (103x)/100xx102/100xx101/100`
`=Rs.(101xx102xx102)/(100xx100xx100).x`
As per questioni `(101xx102xx103)/(100xx100xx100).x=15916.59`
`impliesx=(15916.59xx100xx100xx100)/(101xx102xx103)`
`impliesx=15000`
`:.` The required sum of money `=Rs. 15000`
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