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.
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