Determine the rate of interest for a sum that becomes 216/125 times of itself in 1 ½ years, compounded semi-annually.
Solution:
Consider principal (P) = x
Amount (A) = 216/125 x
Period (n) = 1 ½ years = 3 half years
Take rate percent per year = 2r% and r% half yearly
We know that
A/P = (1 + r/100)n
Substituting the values
216x/125x = (1 + r/100)3
By further calculation
(1 + r/100)3 = 216/125 = (6/5)3
So we get
1 + r/100 = 6/5
r/100 = 6/5 – 1 = 1/5
By cross multiplication
r = 100 × 1/5 = 20%
So the rate percent per year = 2 × 20 = 40%
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