A sum compounded annually becomes 25/16 time of itself in two years. Determine the rate of interest per annum.
Solution:
Consider sum (P) = x
Amount (A) = 25/16x
Period (n) = 2 years
We know that
A/P = (1 + r/100)n
Substituting the values
25x/16x = (1 + r/100)2
By further calculation
(1 + r/100)2 = (5/4)2
So we get
1 + r/100 = 5/4
r/100 = 5/4 – 1/1 = 1/4
By cross multiplication
r = 100 × ¼ = 25
Hence, the rate of interest is 25% p.a.
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