If ₹ 40000 amounts to ₹ 48620.25 in 2 years, compound interest payable half-yearly, find the rate of interest per annum.
Solution:
It is given that
Principal (P) = ₹ 40000
Amount (A) = ₹ 48620.25
Period (n) = 2 years = 4 half years
Consider rate of interest = r% p.a. = r/2% half yearly
We know that
A/P = (1 + r/100)n
Substituting the values
48620.25/40000 = (1 + r/200)4
By further calculation
(1 + r/200)4 = 4862025/ (100 × 40000) = 194481/160000
So we get
(1 + r/200)4 = (21/20)4
It can be written as
1 + r/200 = 21/20
r/200 = 21/20 – 1 = 1/20
By cross multiplication
r = 200 × 1/20 = 10
Hence the rate of interest per annum is 10%.
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