If the simple interest on a sum of money at 10% per annum for 3 years is Rs. 1500, then the compound interest on the same sum at the same rate for the same period is
Simple interest = Rs.1500
Interest rate = 10% per annum
Time = 3 years
Simple interest (SI) = PRT/100 [where, P = Present value
R = Interest rate
∴ 1500 = (P × 10 × 3)/100 T = Time]
⇒ 1500 = P × 30/100
⇒ 1500 = P × 3/10
⇒ P = 1500 × 10/3
⇒ P = 500 × 10
⇒ P = 5000
∴ Sum = Rs.5000
Now,
Amount (A) = P (1 + R/100)n [Where, P = Present value
R = Annual interest rate
n = Time in years]
∴ A = 5000 [1 + 10/100]3
⇒ A = 5000 [1 + 1/10]3
⇒ A = 5000 [11/10]3
⇒ A = 5000 × 11/10 × 11/10 × 11/10
⇒ A = 5000 × 1331/1000
⇒ A = 5 × 1331
⇒ A = 6655
∴ Amount = Rs.6655
∴ Compound interest = Rs.(6655 – 5000)
= Rs.1655