If the simple interest on a sum of money at 10% per annum for 3 years

1.	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 A. Rs. 1655 B. Rs. 1155 C. Rs. 1555 D. Rs. 1855
Answer» 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

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 A. Rs. 1655 B. Rs. 1155 C. Rs. 1555 D. Rs. 1855

Answer»

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