Question : The Simple interest and Compound interest that can be earned in two years at the same rate are Rs. 1,000 and Rs. 1,040, respectively. What is the rate (percent per annum) of interest?
Option 1: 9
Option 2: 10
Option 3: 8
Option 4: 11
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Correct Answer: 8
Solution :
Given: The Simple interest and Compound interest that can be earned in two years at the same rate are Rs. 1,000 and Rs. 1,040, respectively.
The Simple Interest remains the same every year.
Simple interest for 2 years = Rs. 1,000
$\therefore$ Simple interest for 1 years = $\frac{1000}{2}$ = Rs. 500
Let the rate be $R$.
The difference between compound interest and simple interest for two years is equal to the interest in the first year's interest.
So, 40 = $\frac{R×500}{100}$
$\therefore R = 8$%
Hence, the correct answer is 8.
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