Question
The extra interest earned from compound interest over
simple interest on a sum of money after 2 years (with interest compounded semi-annually) is Rs. 972. If the yearly interest rate is 12%, determine the principal.Solution
ATQ,
Let the principal be Rs. P Rate = 12% p.a. Time = 2 years Simple Interest (SI) = (P Γ 12 Γ 2)/100 = Rs. (24P/100) = 0.24P Compound Interest (CI) (semi-annually): Half-yearly rate = 12/2 = 6% Number of half-years = 2 Γ 2 = 4 CI = P Γ {(1.06)β΄ β 1} = P Γ (1.2625 β 1) = 0.2625P Now, CI β SI = 972 β 0.2625P β 0.24P = 972 β 0.0225P = 972 β P = 972 / 0.0225 = Rs. 43,200
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