Question : A moneylender claims he lends money at a simple rate of interest of 8% per annum. But he cleverly includes the interest amount in the principal when he calculates it every six months. The effective Rate of interest becomes:
Option 1: 8.16%
Option 2: 8.2%
Option 3: 8.8%
Option 4: 8.25%
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Correct Answer: 8.16%
Solution :
Let the amount lent be Rs. 100.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
Simple Interest for first 6 months = $\frac{100\times 8\times \frac{1}{2}}{100}$ = Rs. 4
Increased principal = Rs. 104
Simple Interest for next 6 months = $\frac{104\times 8\times \frac{1}{2}}{100}$ = Rs. 4.16
Total Interest = 4 + 4.16 = Rs. 8.16
So, Interest rate = $\frac{8.16}{100}\times 100$ = 8.16%
Hence, the correct answer is 8.16%.
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