Vikram borrowed ₹ 20000 from a bank at 10% per annum simple interest. He lent it to his friend Venkat at the same rate but compounded annually. Find his gain after 2 ½ years.
Solution:
First case-
Principal = ₹ 20000
Rate = 10% p.a.
Period = 2 ½ = 5/2 years
We know that
Simple interest = Prt/100
Substituting the values
= (20000 × 10 × 5)/ (100 × 2)
= ₹ 5000
Second case-
Principal = ₹ 20000
Rate = 10% p.a.
Period = 2 ½ years at compound interest
We know that
Amount = P (1 + r/100)n
Substituting the values
= 20000 (1 + 10/100)2 (1 + 10/ (2 × 100))2
By further calculation
= 20000 × 11/10 × 11/10 × 21/20
= ₹ 25410
Here
Compound Interest = A – P
Substituting the values
= 25410 – 20000
= ₹ 5410
So his gain after 2 years = CI – SI
We get
= 5410 – 5000
= ₹ 410
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