A certain sum amounts to ₹ 9036 after 3 years and to ₹ 11484 after 7 years at the same rate percent per annum at simple interest. What will be the compound interest (in Rs) (to the nearest ₹) on the same sum for 2 years at the double rate of interest if interest is compounded annually?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2656.
Given:
A certain sum amounts to ₹ 9036 after 3 years and to ₹ 11484 after 7 years at the same rate percent per annum at simple interest
Formula used:
SI = PRT/100 ---- (1)
CI = P(1 + R/100)T - P ----- (2)
Where SI = simple interest, CI = compound interest, P = principle, R = rate and T = time
Calculations:
Interest of 4 years = 11484 - 9036 = 2448
Interest of 3 years = 2248 × (3/4) = 1836
Sum = 9036 - 1836 = 7200
Using equation (1), we get
⇒ 1836 = (7200 × R × 3)/100
⇒ 1836 = 216 × R
⇒ R = 8.5
Now, using equation (2),
⇒ CI = 7200(1 + 8.5/100)2 - 7200
⇒ CI = 7200(117/100)2 - 7200
⇒ CI = 7200(13689/10000) - 7200
⇒ CI = 7200(3689/10000)
⇒ CI = 2656 (approx.)