If a money lender charges interest at the rate of Rs. 5 per Rs. 100 ev...
Effective Rate of Interest per Annum
When a money lender charges interest at a certain rate per quarter and is payable in advance, the effective rate of interest per annum can be calculated using the following formula:
Effective Rate of Interest per Annum = [(1 + r/n)^n - 1] x 100
Where,
r = rate of interest per quarter
n = number of quarters in a year (4)
100 = to convert the decimal to percentage
Calculation:
In this case, the money lender charges Rs. 5 per Rs. 100 every quarter. So, the rate of interest per quarter (r) can be calculated as follows:
r = (5/100) x 100 = 5%
Now, substituting the values of r and n in the formula, we get:
Effective Rate of Interest per Annum = [(1 + 5/100/4)^4 - 1] x 100
= [(1.0125)^4 - 1] x 100
= (1.0537 - 1) x 100
= 0.0537 x 100
= 5.37%
Therefore, the money lender charges an effective rate of interest of 5.37% per annum.
Explanation:
When a money lender charges interest at a certain rate per quarter and is payable in advance, the borrower has to pay the interest amount for the entire year in advance. So, to calculate the effective rate of interest per annum, we need to take into account the compounding effect of quarterly interest payments.
The formula used to calculate the effective rate of interest per annum takes into account this compounding effect. It uses the concept of annual equivalent rate (AER), which is the rate of interest that would give the same return if the interest was compounded annually.
In this case, the money lender charges Rs. 5 per Rs. 100 every quarter, which means that the rate of interest per quarter is 5%. Using the formula for effective rate of interest per annum, we can calculate the AER as 5.37%. This means that if the borrower takes a loan of Rs. 100 and pays back Rs. 110.37 at the end of the year, the effective rate of interest charged by the money lender would be 5.37%.
If a money lender charges interest at the rate of Rs. 5 per Rs. 100 ev...
Given:
Interest rate per quarter = 5 rupees per 100 rupees
Interest rate per annum = ?
To find the effective rate per annum, we need to consider that the interest is payable in advance. This means that the borrower pays the interest at the beginning of each quarter.
Since the interest is payable in advance, we need to compound the interest for four quarters in a year.
The interest rate of 5 rupees per 100 rupees can be written as 5% per quarter.
To calculate the effective annual rate, we can use the formula:
Effective Annual Rate = (1 + Interest Rate)^Number of Compounding Periods - 1
Plugging in the values:
Effective Annual Rate = (1 + 0.05)^4 - 1
= 1.05^4 - 1
= 1.21550625 - 1
= 0.21550625
Converting the decimal to a percentage:
Effective Annual Rate = 0.21550625 * 100
= 21.550625%
Therefore, the effective rate charged by the money-lender per annum, considering the interest payable in advance, is approximately 21.550625%.
Based on this calculation, the correct answer is 22.8% from the given options.
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