Determine the comparable interest rate for a $50,000 loan when the quoted information is 10.6% + 0.5 pt + $400. (Round your answer to two decimal places.)
To determine the comparable interest rate for the loan, we need to consider the three components of the quoted information - the stated interest rate, the number of points, and any additional fees.
1. Stated Interest Rate: The quoted information states that the interest rate is 10.6%. This means that for every year, the borrower will be charged 10.6% of the loan amount as interest.
2. Points: Points are a one-time fee paid upfront to the lender and are typically expressed as a percentage of the loan amount. In this case, it mentions an additional 0.5 pt. "Pt" is short for "point." One point is equivalent to 1% of the loan amount. So, 0.5 pt is 0.5% of the loan amount.
3. Additional Fees: The quoted information also includes an additional fee of $400.
Now, let's calculate the comparable interest rate:
Step 1: Calculate the total cost of points:
Points = 0.5% of $50,000
Points = 0.005 * $50,000
Points = $250
Step 2: Add the additional fees:
Additional Fees = $400
Step 3: Calculate the total cost of the loan:
Total Loan Cost = Cost of Interest + Cost of Points + Additional Fees
Total Loan Cost = $50,000 * (10.6% + 0.5%) + $250 + $400
Total Loan Cost = $50,000 * 0.106 + $250 + $400
Total Loan Cost = $5,300 + $250 + $400
Total Loan Cost = $5,950
Step 4: Calculate the comparable interest rate:
Comparable Interest Rate = Total Loan Cost / Loan Amount
Comparable Interest Rate = $5,950 / $50,000
Comparable Interest Rate = 0.119 or 11.9% (rounded to two decimal places)
Therefore, the comparable interest rate for the $50,000 loan, considering the stated interest rate, points, and additional fees, is approximately 11.9%.