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Question
On what sum of money will the compound interest for `2 1/2` years at `12 1/2`% per annum amount to Rs 82,734.37?
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Solution
P =x ; t = `2 1/2` years ; r = `12 1/2` % = `25/2` % ; A = Rs (x + 82734.37)
`"A" = "P" (1 + "r"/100)^"n"`
Rs (x + 82,734.37 ) = x `(1 + 25/(2 xx 100))^2 (1 + 25/(2 xx 100))^(1/2)`
Rs (x + 82, 734.37) - x `(1 +25/(2 xx 100))^2 (1 + 25/(2 xx 100))^(1/2)`
Rs ( x + 82,734.37) = x × 1.125 × 1.125 × `(1 + 1/2 xx 1/8)`
Rs (x + 82,734.37) - x × 1.125 × 1.125 × 1.0625
Rs (x + 82, 734.37) - 1.344727 x
0.344727 x - Rs 82,734.37
x = Rs 2,39,999.7 = Rs 2,40, 000
On Rs 2,40,000 the C.I. for `2 1/2` years at `12 1/2` % will be Rs 82,734.37
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