# The difference be

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

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