Determine the comparable interest rate for a $50,000 loan when the quoted information is 11.8% + 0.5 pt + $300. (Round your answer to two decimal places.)
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To determine the comparable interest rate for a $50,000 loan, we need to break down the quoted information into its components.
The given information includes:
- 11.8% as the base interest rate
- 0.5 points as an additional fee
- $300 as an upfront cost
To calculate the comparable interest rate, we need to consider both the additional fee and upfront cost as part of the loan.
Step 1: Calculate the additional fee:
To calculate the additional fee in dollars, we multiply the loan amount by the points percentage.
0.5 points = 0.5% = 0.005 (in decimal form)
Additional fee = $50,000 * 0.005 = $250
Step 2: Calculate the total cost of the loan:
The total cost of the loan is the sum of the base amount, additional fee, and upfront cost.
Total cost = Base amount + Additional fee + Upfront cost
Total cost = $50,000 + $250 + $300 = $50,550
Step 3: Calculate the interest rate:
To calculate the comparable interest rate, we need to know the total loan cost over the loan term.
Assuming the loan term is not given, let's consider it as 1 year for simplicity.
Comparable interest rate = (Total cost - Loan amount) / Loan amount
Comparable interest rate = ($50,550 - $50,000) / $50,000
Comparable interest rate = $550 / $50,000
Now, let's convert to a percentage by multiplying by 100:
Comparable interest rate = ($550 / $50,000) * 100
Comparable interest rate = 1.1%
Therefore, the comparable interest rate for the $50,000 loan, given the quoted information of 11.8% + 0.5 points + $300, is approximately 1.10% when rounded to two decimal places.