Question : The simple interest on a sum of money at 10% per annum for 2 years is 8,100. Compounded annually, what would be the compound interest (in ) on the same sum for the same period at the same rate of interest?
Option 1: 8,100
Option 2: 8,505
Option 3: 8,715
Option 4: 9,000
Correct Answer: 8,505
Solution :
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
According to the question
$⇒ 8100 = \frac{\text{Principal}×10×2}{100}$
$\therefore$ Principal $= 40500$
Now,
$\text{Total Amount}$
$=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$ = 40500({1+ \frac{10}{100})^2}$
$ = 40500({ \frac{11}{10})^2}$
$ = 40500×{ \frac{121}{100}}$
$=49005$
$\therefore$ Compound Interest = Amount – Principal = 49005 – 40500 = 8505
Hence, the correct answer is 8505.
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