The simple interest on a sum of money for 2 years at 8% per annum is R

1.	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?
Answer» 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

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?

Answer»

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