The compound interest compounded annually on a sum of money for 2 years is Rs. 1,128.6 and the simple interest on the same sum for the same period is Rs. 1,080. What is the difference between the compound interest compounded annually and the simple interest for 3 years?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. Rs.150.174.
Given:
The compound interest compounded annually on a sum of money for 2 years is Rs. 1,128.6 and the simple interest on the same sum for the same period is Rs. 1,080
Formula used:
SI = PRT/100
CI = P(1 + R/100)T - P
Where, SI = Simple interest, CI = compound interest
P = Principle, R = rate and T = time
Calculations:
SI of 1 years = 1080/2 = 540
Difference between SI and CI for 2 years = 1128.6 - 1080 = 48.6
R = (48.6 × 100)/(540) = 9%
Using equation (1), we get
⇒ 1080 = (P × 9 × 2)/100
⇒ P = 6000
Effective rate for 2 years (compound interest) = 9 + 9 + .81 = 18.81%
Effective rate for 3 years (Compound interest) = 18.81 + 9 + (18.81 × 9)/100 = 29.5029%
The effective rate for 3 years (Simple interest) = 27%
Difference in rate of interest = 29.5029% - 27 = 2.5029%
Required difference of interest = (6000 × 2.5029 × 1)/100 = 150.174