Question
On a certain principal, the difference between compound
interest (compounded annually) and simple interest at the same annual rate for 2 years is Rs 72. If the rate of interest is 6% per annum, what is the principal (in rupees)?Solution
ATQ, Let principal = P, rate = r = 6% = 0.06. For 2 years: Simple interest = P × 2r = 2Pr. Compound interest = P[(1 + r)² − 1] = P(2r + r²). Difference = CI − SI = P(2r + r² − 2r) = P r². So P × (0.06)² = 72 P × 0.0036 = 72 ⇒ P = 72 / 0.0036 = 20,000.
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