If the simple interest on a sum of money at 10% per annum for 3 years is Rs. 1500, A. Rs. 1655 B. Rs. 1155 C. Rs. 1555 D. Rs. 1855

Question

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 1

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