The simple interest on a certain sum for 2 years at 10% per annum is half of the compound interest on a sum of ₹ 5,000 for 2 years at 10% per annum, interest compounded yearly. What is the sum placed on simple interest?

Explanation

Given: The simple interest on a certain sum for 2 years at 10% per annum is half of the compound interest on a sum of ₹ 5,000 for 2 years at 10% per annum. Concept used: Simple Interest, SI = (P × R × T)/100 Amount = P + SI where P = Principal amount R = Rate of interest per year T = Time in years In case of the compound interest, Amount = P(1 + R/100) N CI = P(1 + R/100) N- P where P = Principal amount R = Rate of interest per year N = Time in years Calculation: Let the principal sum placed on simple interest be P. Simple interest incurred = (P × 10 × 2)/100 = 0.2P Compound interest incurred ⇒ 5000(1 + 10/100) 2 - 5000 ⇒ 1.21 × 5000 - 5000 ⇒ 0.21 × 5000 = Rs. 1050 According to the question, 0.2P = 1050/2 ⇒ 0.2P = 525 ⇒ P = 525/0.2 ⇒ P = 2625 ∴ The sum placed on simple interest is Rs. 2625.