Question : The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Option 1: Rs. 520
Option 2: Rs. 550
Option 3: Rs. 500
Option 4: Rs. 515
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Correct Answer: Rs. 500
Solution :
Rate, R = 10%
Compound interest = Rs. 525
Term, n = 2 years
Compound interest after 2 years = $P[(1+\frac{R}{100})^{2} –1]$
⇒ 525 = $P[(1+\frac{10}{100})^{2} –1)]$
⇒ 525 = $P[(1.21 –1]$
$\therefore$ P = $\frac{525}{0.21}$ = Rs. 2500
Simple interest after n years = $\frac{PnR}{100}$
Time = 2n = 4 years
Rate = R ÷ 2 = 5%
$\therefore$ Simple interest after 4 years = $\frac{2500×4×5}{100}$ = Rs. 500
Hence, the correct answer is Rs. 500.
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