A certain sum amounts to ₹9,036 after 3 years and to ₹11484 after 7 years at the same rate per cent per annum at simple interest. What will the compound interest( in ₹) (to the nearest ₹) on the same sum for 2 years at the double rate of interest if interest is compounded annually?

Explanation

Given: A certain sum amounts to ₹9,036 after 3 years and to ₹11484 after 7 years at the same rate per cent per annum at simple interest Concept used: S.I = (P × T × R)/100 C.I = P[(1 + R/100) T- 1] Here, P = Sum R = Rate T = Time Calculation: Interest of the 4 years = 11484 - 9036 ⇒ 2448 So, interest for 3 years = 2448 × (3/4) ⇒ 1836 So, sum = 9036 - 1836 ⇒ 7200 Let the rate of interest be R So, 1836 = (7200 × R × 3)/100 ⇒ R = 1836/(72 × 3) ⇒ R = 8.5 Now, C.I = 7200[(1 + 17/100) 2- 1] ⇒ 7200[(117/100) 2 - 1] ⇒ 7200[(13689/10000) - 1] ⇒ 7200[(13689 - 10000)/10000)] ⇒ 7200[3689/10000 ] ⇒ 2656.08 ≈ 2656 ∴ The compound interest( in ₹) (to the nearest ₹) is 2656.