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
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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