The simple interest on a sum of money for 2 years at 8% per annum is Rs. 2400. What will be the compound interest on that sum at the same rate and for the same period?
Simple interest = Rs.2400
Interest rate = 8% per annum
Time = 2 years
Simple interest (SI) = PRT/100 [where, P = Present value
R = Interest rate
∴ 2400 = (P × 8 × 2)/100 T = Time]
⇒ 2400 = P × 16/100
⇒ 2400 = P × 4/25
⇒ P = 2400 × 25/4
⇒ P = 600 × 25
⇒ P = 15000
∴ Sum = Rs.15000
Now,
Amount (A) = P (1 + R/100)n [Where, P = Present value
R = Annual interest rate
n = Time in years]
∴ A = 15000 [1 + 8/100]2
⇒ A = 15000 [1 + 2/25]2
⇒ A = 15000 [27/25]2
⇒ A = 15000 × 27/25 × 27/25
⇒ A = 600 × 27 × 27/25
⇒ A = 24 × 27 × 27
⇒ A = 17496
∴ Amount = Rs.17496
∴ Compound interest = Rs.(17496 – 15000)
= Rs.2496