The compound interest (compounding half-yearly) received on Rs. 10000 for 1.5 years is Rs. 3676.31. What is the rate of interest per annum?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 22%.
We know that,
A = P(1 + R/2)2T
here, A = Amount, P = Principal, R = Rate, and T = Time
Total Amount A = P + C.I.
⇒ A = 10000 + 3676.31
⇒ A = 13676.31
Now,
⇒ 13676.31 = 1000(1 + R/200)2 × 1.5
⇒ 13676.31 = 1000(1 + R/200)3
⇒ 13676.31/1000 = (1 + R/200)3
⇒ 1.367631 = (1 + R/200)3
⇒ ∛1.367631 = (1 + R/200)
⇒ 1 + R/200 = 1.1
⇒ R/200 = 1.1 - 1
⇒ R/200 = 0.1
⇒ R = 20%
Hence, the rate of interest per annum is 20%