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Question
A certain sum due 3 months hence is `21/20` of the present worth, what is the rate of interest?
Solution
Given, S.D. =`21/20 xx "P.W."`, n = `3/12 = 1/4` years
Since, S.D. = P.W. + T.D.
∴ `21/20 "P.W." = "P.W." + "T.D."`
∴ `21/20 "P.W." - "P.W." = "T.D."`
∴ T.D. = `1/20` P.W.
Also, T.D. = `("P.W." xx "n" xx "r")/100`
∴ `1/20 "P.W." = ("P.W." xx 1/4 xx "r")/100`
∴ `1/20 = "r"/(4 xx 100)`
∴ r = `400/20 = 20 %` p.a.
∴ Rate of interest is 20% p.a.
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