The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% per annum is Rs. 90.

Find the sum.

Let sum = P

Interest rate = 6% per annum

Time = 2 years

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

R = Annual interest rate

T = Time in years]

∴ SI = (P × 6 × 2)/100

⇒ SI = 3P/25 __________ (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 + 6/100)² - P

⇒ CI = P (1 + 3/50)² - P

⇒ CI = P (53/50)² - P

⇒ CI = (2809P/2500)- P

⇒ CI = (2809P – 2500P)/2500

⇒ CI = 309P/2500 ______ (ii)

Now,

CI – SI = (309P/2500) – (3P/25)

⇒ 90 = (309P/2500) – (3P/25) [Given, CI – SI = 90]

⇒ 90 = (309P – 300P)/2500

⇒ 90 = 9P/2500

⇒ P = 90 × 2500/9

⇒ P = 10 × 2500

⇒ P = 25000

∴ Sum = Rs.25000