To borrow $2,200, you are offered an add-on interest loan at 10.2 percent with 12 monthly payments
Equal payment
Compute the EAR of the loan.
EAR
Oh, the EAR! I'm not talking about the one on your head, but the Effective Annual Rate in this case. Now, let's do some math magic and find out the EAR for this loan.
First, let's make sure we convert that add-on interest rate to its equivalent EAR. With an add-on interest loan, the interest is calculated on the original principal, not the outstanding balance. So, if you're borrowing $2,200, with a 10.2 percent add-on interest, the annual interest would be $2,200 * 0.102 = $224.40.
Now, we need to figure out how much you'll really end up paying each year. Since it's a 12-month loan with equal payments, simply multiply the monthly payment by 12. Let's say the monthly payment is $200, then the annual payment would be $200 * 12 = $2,400.
Finally, to calculate the EAR, we need to factor in the compounding that occurs over the year. The formula for EAR is (1 + r/n)^(n*t) - 1, where r is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, the nominal interest rate is 10.2 percent divided by 100, which gives us 0.102. The compounding periods per year is once per month, so n = 12. The time period is 1 year, so t = 1.
Plugging those values into the formula, we get (1 + 0.102/12)^(12*1) - 1. After crunching the numbers, the result is approximately 0.1067, or 10.67 percent.
So, the EAR of this loan is approximately 10.67 percent. It's always good to know the whole picture when you're dealing with loans.
To calculate the Effective Annual Rate (EAR) of the loan, you need to consider the add-on interest formula.
The formula for add-on interest is:
Total Interest = Principal x Interest Rate x Number of Periods
In this case, the principal is $2,200, the interest rate is 10.2%, and the loan term is 12 months.
First, let's calculate the total interest:
Total Interest = $2,200 x 10.2% x 12 = $2,640
Next, we need to add the total interest to the principal to find the total amount to be repaid:
Total Repayment Amount = Principal + Total Interest = $2,200 + $2,640 = $4,840
Finally, we can use the total repayment amount to calculate the EAR using the following formula:
EAR = [(1 + (Total Interest / Principal))^(365 / Number of Days)] - 1
Since the loan term is in months and there are 365 days in a year, the number of days is 365.
EAR = [(1 + ($2,640 / $2,200))^(365 / 365)] - 1
EAR = [(1 + 1.2)^(1)] - 1
EAR = (2.2) - 1
EAR = 1.2
Therefore, the Effective Annual Rate (EAR) for the loan is 120%.
To compute the effective annual rate (EAR) of the loan, follow these steps:
Step 1: Find the nominal interest rate (NIR):
The nominal interest rate (NIR) is the stated interest rate of the loan. In this case, the NIR is 10.2 percent.
Step 2: Determine the frequency of compounding:
The frequency of compounding refers to how often the interest is added to the loan balance. Since it is a monthly payment loan, the compounding occurs on a monthly basis.
Step 3: Convert the NIR to a decimal:
To calculate the EAR, we need to convert the nominal interest rate to a decimal. Divide the NIR by 100:
10.2 percent / 100 = 0.102
Step 4: Determine the number of compounding periods per year:
Since the compounding occurs monthly, the number of compounding periods per year is 12 (12 monthly payments).
Step 5: Apply the EAR formula:
The formula to calculate the EAR is as follows:
EAR = (1 + (NIR / m))^m - 1
Where:
- NIR: nominal interest rate (in decimal form)
- m: number of compounding periods per year
Substituting the values into the formula:
EAR = (1 + (0.102 / 12))^12 - 1
Step 6: Calculate the EAR:
Using a calculator or spreadsheet, evaluate the expression:
EAR = (1 + (0.102 / 12))^12 - 1 ≈ 10.55%
Therefore, the effective annual rate (EAR) of the loan is approximately 10.55%.