Question : A certain amount of money earns Rs. 540 as a simple interest in 3 years. If it earns a compound interest of Rs. 376.20 at the same rate of interest in 2 years, find the amount (in Rs.):
Option 1: Rs. 1600
Option 2: Rs. 1800
Option 3: Rs. 2000
Option 4: Rs. 2100
Correct Answer: Rs. 2000
Solution : Given: Simple interest (SI) = Rs. 540 Period of simple interest = 3 years Compound interest (CI) = Rs. 376.20 Period of compound interest = 2 years Simple interest for 1 year = $\frac{1}{3}×540$ = Rs. 180 Simple interest for 2 year = $\frac{2}{3}×540$ = Rs. 360 CI – SI = 376.20 – 360 = Rs. 16.20 Rate of interest = $\frac{16.20}{180}×100$ = 9% per annum Principal = $\frac{\text{S.I}×100}{\text{Time×Rate}}$ Therefore, Principal = $\frac{180×100}{1×9}$ = Rs. 2000 Hence, the correct answer is Rs. 2000.
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