Question

The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is Rs. 93. Find the sum.

Answer 1

Let sum = P 

Interest rate = 10% per annum 

Time = 3 years 

Simple interest (SI) = PRT/100 [Where, P = Present value 

R = Annual interest rate 

T = Time in years] 

∴ SI = (P × 10 × 3)/100 

⇒ SI = 3P/10 ______ (i) 

Compound interest (CI) = P (1 + R/100)ⁿ - P [Where, P = Present value 

R = Annual interest rate 

n = Time in years] 

∴ CI = P (1 + 10/100)³ - P 

⇒ CI = P (1 + 1/10)³ - P 

⇒ CI = P (11/10)3 - P 

⇒ CI = (1331P/1000)- P 

⇒ CI = (1331P – 1000P)/1000 

⇒ CI = 331P/1000 ______ (ii) 

Now, 

CI – SI = (331P/1000) – (3P/10) 

⇒ 93 = (331P/1000) – (3P/10) [Given, CI – SI = 93] 

⇒ 93 = (331P – 300P)/1000 

⇒ 93 = 31P/1000 

⇒ P = 93 × 1000/31 

⇒ P = 3 × 1000 

⇒ P = 3000 

∴ Sum = Rs.3000