Find the time period of investment.

₹ 16000 invested at 10% p.a., compounded semi-annually, amounts to ₹ 18522, find the time period of investment.

Solution:

It is given that
Principal (P) = ₹ 16000
Amount (A) = ₹ 18522
Rate = 10% p.a. or 5% semi-annually
Consider period = n half years
We know that
A/P = (1 + r/100)ⁿ
Substituting the values
18522/16000 = (1 + 5/100)ⁿ
By further calculation
9261/8000 = (21/20)ⁿ
So we get
(21/20)³ = (21/20)ⁿ
n = 3 half years
Here
Time = 3/2 = 1 ½ years

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