A sum lend at compound interest amounts to 72.8% more than itself in 3 years, interest compounded annually at a certain rate percent per annum. What will be the compound interest (in ₹) on a sum of ₹ 18,000 for 1(1/2) years at the same rate if the interest is compounded six- monthly?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 5,958.
Given:
A sum lend at compound interest amounts to 72.8% more than itself in 3 years, interest compounded annually at a certain rate percent per annum
P = 18000 and time = 1(1/2) years
Formula used:
Amount = Principle + Interest
Amount = P(1 + R/100)T ------ (1)
Where P = principle, R = rate and T = time
Calculations:
Let the principle and rate of interest be P and R
According to the question;
⇒ P(1 + R/100)3 = P + P × 72.8%
⇒ P(1 + R/100)3 = P + P × 0.728
⇒ (1 + R/100)3 = 1 + 0.728
⇒ (1 + R/100)3 = 1.728 (cube root on both sides)
⇒ 1 + R/100 = 1.2
⇒ R/100 = 0.2
⇒ R = 20
Now calculating compound interest on a sum of Rs. 18000 when time is 1(1/2) years and rate is 20%
As interest is compounded half yearly so Rate = 20/2 = 10% and time = 1.5 × 2 = 3 years
⇒ Compound interest = 18000(1 + 10/100)3 - 18000
⇒ 18000(1.1)3 - 18000
⇒ 18000 × 1.331 - 18000
⇒ 23958 - 18000 = 5958