Determine the comparable interest rate for $40,000 loan when the quoted information is 10.9%+0.5pt+$300.(round your answer to two decimals places.)
To determine the comparable interest rate for a $40,000 loan with quoted information of 10.9% + 0.5pt + $300, we need to break down the different components.
First, let's understand what each part of the quoted information represents:
- 10.9%: This is the base interest rate.
- 0.5pt: "pt" stands for points, which are an upfront fee expressed as a percentage of the loan amount. Each point is equal to 1% of the loan amount. In this case, it is 0.5 points.
- $300: This is an additional fee or cost.
To calculate the comparable interest rate, we need to add up these components.
Step 1: Calculate the points for a $40,000 loan.
Since each point is 1% of the loan amount, we have 0.5 points, which is equal to 0.005 (0.5/100) times $40,000.
Points = 0.005 * $40,000 = $200
Step 2: Add up the base interest rate, points, and additional fee.
Comparable interest rate = Base interest rate + Points + Additional fee
Comparable interest rate = 10.9% + $200 + $300
Step 3: Convert the numbers to decimal form.
10.9% = 0.109
Points = $200/$40,000 = 0.005
Additional fee = $300/$40,000 = 0.0075
Step 4: Calculate the comparable interest rate.
Comparable interest rate = 0.109 + 0.005 + 0.0075
Step 5: Round the answer to two decimal places.
Comparable interest rate = 0.1215 (rounded to two decimal places)
Therefore, the comparable interest rate for the $40,000 loan based on the quoted information of 10.9% + 0.5pt + $300 is approximately 12.15%.