A money lender charges Rs. 10 for Rs. 100 per month in advance then effective rate of interest per annum charged by money lender is: [given $(\frac{10}{9})^{12} = 3.541$]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25.41%
Note: there is a mistake in this question of NTA. The correct answer should be 254.1% which is not there in any of the options. the detailed calculation is given below:
Normally, if you borrow ₹100 and pay ₹10 interest at the end of the month, the rate is $10\%$. However, because the money lender charges the interest in advance, you don't actually get ₹100.
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Principal Borrowed: ₹100
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Interest Paid Upfront: ₹10
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Actual Amount Received: $100 - 10 = ₹90$
Since you are paying ₹10 to use ₹90 for one month, the monthly interest rate ($r$) is:
$$r = \frac{10}{90} = \frac{1}{9}$$
The effective annual rate accounts for compounding monthly. The formula for the effective rate is:
$$E = (1 + r)^n - 1$$
Where:
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$r = \frac{1}{9}$
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$n = 12$ months
Using the value given in the question $(\frac{10}{9})^{12} = 3.541$:
To get the percentage, multiply by 100: $$E = 2.541 \times 100 = 254.1\%$$