A $5000 loan has a stated rate of 10% but it will be paid off in 12 equal monthly payments. What is the APR on the loan?
To calculate the APR (Annual Percentage Rate) on a loan, you need to consider both the stated interest rate and the frequency of compounding. In this case, since the loan is being paid off in 12 equal monthly payments, the APR can be calculated using the formula:
APR = (1 + r/n)^n - 1
Where:
r = stated interest rate (as a decimal)
n = number of compounding periods per year
In this scenario, the stated interest rate is 10%. However, to calculate the APR, you need to express it as a decimal:
r = 10% = 0.10
Next, you need to determine the number of compounding periods per year. Since the loan is being paid off in 12 equal monthly payments, there are 12 compounding periods in a year:
n = 12
Plugging in the values into the formula:
APR = (1 + 0.10/12)^12 - 1
Using a calculator or a spreadsheet, evaluate the expression inside the parentheses first: (1 + 0.10/12) = 1.0083333.
Raise this value to the power of 12 and subtract 1 from the result:
APR = (1.0083333)^12 - 1
Calculating the expression within the parentheses: (1.0083333)^12 = 1.1047139
Subtracting 1 from the result: 1.1047139 - 1 = 0.1047139
Therefore, the APR on the $5000 loan with a stated interest rate of 10% and 12 equal monthly payments is approximately 10.47%.