The sum of the simple interest and the compound interest on ₹ 5,600 at the same rate of interest per annum for two years is ₹ 2,061.36, when in the case of compound interest, it is compounded annually. What is the rate of interest per annum?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 9%
Formula used:
SI = PRT/100 and
CI = P(1 + R/100)T - P
Where, CI = Compound interest, SI = Simple interest, P = principal, R = rate and T = Time
Calculations:
According to the question;
⇒ SI + CI = PRT/100 + P(1 + R/100)T - P
⇒ 2,061.36 = (5600 × R × 2)/100 + 5600(1 + R/100)2 - 5600
⇒ 2061.36/5600 = 2R/100 + 1 + 2R/100 + R2/10000 - 1
⇒ 3681/100 = 4 × R + R2/100
⇒ R2 + 400R - 3681 = 0
⇒ (R - 9)(R + 409) = 0
⇒ R = 9%