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Question
In how many years ₹ 700 will amount to ₹ 847 at a compound interest rate of 10 p.c.p.a.
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Solution
Here, P = Principal = ₹ 700
A = Amount = ₹ 847
R = 10 %
N = N years
A = P`(1 + "R"/100)^"N"`
∴ `847 = 700(1 + 10/100)^"N"`
∴ `847 = 700((100 + 10)/100)^"N"`
∴ `847 = 700(110/100)^"N"`
∴ `847 = 700(11/10)^"N"`
∴ `847/700 = (11/10)^"N"`
∴ `(121 xx 7)/(100 xx 7) = (11/10)^"N"`
∴ `121/100 = (11/10)^"N"`
∴ `(11/10)^2` = `(11/10)^"N"`
∴ N = 2 ...[If an = am, then n = m]
Hence, the number of years is 2 years.
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