Determine the comparable interest rate for a $50,000 loan when the quoted information is 12.2% + 0.5 pt + $300. (Round your answer to two decimal places.)
To determine the comparable interest rate for the given loan, we need to analyze the different components of the quoted information and calculate the total cost of borrowing. The different components are:
1. The base interest rate: 12.2%
2. The point charge: 0.5 pt
3. The additional fee: $300
Let's break down each component and calculate the total cost of borrowing:
1. Base Interest Rate (Step 1):
The base interest rate is 12.2%. To convert this into a decimal, divide it by 100: 12.2% / 100 = 0.122.
2. The Point Charge (Step 2):
A point is equal to 1% of the loan amount. In this case, the quoted information mentions 0.5 point, so we multiply this by 0.005 (0.5 / 100) to get the decimal form: 0.005.
3. The Additional Fee (Step 3):
The quoted information mentions an additional fee of $300.
Now, let's calculate the total cost of borrowing:
Total Cost of Borrowing (Step 4):
Add up the base interest rate, the point charge, and the additional fee.
Total Cost of Borrowing = Base Interest Rate + Point Charge + Additional Fee
Total Cost of Borrowing = 0.122 + 0.005 + $300
To calculate the comparable interest rate, divide the total cost of borrowing by the loan amount:
Comparable Interest Rate = (Total Cost of Borrowing / Loan Amount) * 100
Comparable Interest Rate = (0.122 + 0.005 + 30000) / 50000 * 100
Simplifying this equation will give you the comparable interest rate for the $50,000 loan.