Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
📊 Let’s Break Down the Problem! 🤔
Step 1: Calculate the Compound Interest (CI) on Rs. 4000 for 2 years at 10% per annum.
CI = P(1 + r/n)^(nt) – P
where P = 4000, r = 10%, n = 1, t = 2
CI = 4000(1 + 0.10/1)^(1*2) – 4000
CI = 4000(1.10)^2 – 4000
CI = 4000(1.21) – 4000
CI = 4840 – 4000
CI = 840
Step 2: Since the Simple Interest (SI) is half the Compound Interest (CI), calculate the SI.
SI = CI / 2
SI = 840 / 2
SI = 420
Step 3: Use the Simple Interest formula to find the principal amount (P).
SI = (P * r * t) / 100
where SI = 420, r = 8%, t = 3 years
420 = (P * 8 * 3) / 100
42000 = P * 24
P = 42000 / 24
P = 1750
The final answer is: The sum placed on simple interest is Rs. 1750. 📈
