Find the rate of interest per annum compounded half-yearly.

Sudarshan invested ₹ 60000 in a finance company and received ₹ 79860 after 1 ½ years. Find the rate of interest per annum compounded half-yearly.

Solution:

It is given that
Principal (P) = ₹ 60000
Amount (A) = ₹ 79860
Period (n) = 1 ½ years = 3 half-years
We know that
A/P = (1 + r/100)ⁿ
Substituting the values
79860/60000 = (1 + r/100)³
By further calculation
(1 + r/100)³ = 1331/1000 = (11/10)³
We get
1 + r/100 = 11/10
r/100 = 11/10 – 1 = 1/10
By cross multiplication
r = 1/10 × 100 = 10% half-yearly
r = 10 × 2 = 20% p.a.
Therefore, the rate of interest per annum compounded half-yearly is 20%.

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