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Question
The difference between simple interest and compound interest compounded annually on a certain sum is Rs.448 for 2 years at 8 percent per annum. Find the sum.
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Solution
Since, C.I.
= A - P
C.I. = `(1 + 8/100)^2 - "P"`
= `"P"(108/100)^2 - "P"`
= `(11664"P")/(10000) - "P"`
= `(11664"P" - 10000"P")/(10000)`
= `(1664"P")/(10000)`
S.I. = `("P" xx 8 xx 2)/(100)`
= `(16"P")/(100)`
Now, C.I. - S.I = Rs.448
⇒ `(1664"P")/(10000) - (16"P")/(100)` = Rs.448
⇒ `(1664"P" - 1600"P")/(10000)` = Rs.448
⇒ 64P = Rs.4480000
⇒ P = Rs.70000
Hence, the sum is Rs.70000.
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