Question : The difference between simple interest and compound interest (compounding of interest is done annually) on a certain sum of money for 3 years at the rate of 20 percent per annum is Rs. 192. What is the sum?
Option 1: Rs 1500
Option 2: Rs 1400
Option 3: Rs 1000
Option 4: Rs 1200
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Correct Answer: Rs 1500
Solution : Simple interest (SI): SI = $\frac{P×R×T}{100}$ Compound interest (CI): CI = {P$(1+\frac{R}{100})^T$ − P] where P = Principal, R = Rate, T = Time According to question CI − SI =192 ⇒ P$(1+\frac{R}{100})^T$ − P − $\frac{P×R×T}{100}$ = 192 ⇒ P$(1+\frac{20}{100})^3$ − P − $\frac{P × 20× 3}{100}$ = 192 ⇒ P$(1+\frac{1}{5})^3$ − P − $\frac{3P}{5}$ = 192 ⇒ $\frac{216P – 125P – 75P}{125}$ = 192 ⇒ $\frac{16P}{125}$ = 192 ⇒ P = $\frac{192 × 125}{16}$ = 1500 Hence, the correct answer is Rs.1500.
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