Determine the comparable interest rate for a $70,000 loan when the quoted information is 10.2% + 0.5 pt + $200. (Round your answer to two decimal places.)
Just need the steps to solve this problem.
your statement
10.2% + .. + $200 makes no sense
you cannot add percentages to dollars
The cash that you get from the loan is 70,000 - 200 - 350 = 69,450. Yet you are paying 10.2% = 7140 interest per year. The true interest rate is
7140/69450 = 10.28%
To determine the comparable interest rate for a $70,000 loan with the quoted information of 10.2% + 0.5 pt + $200, follow these steps:
Step 1: Convert any percentage points to a decimal.
- The quoted information includes 0.5 points. To convert this to a decimal, divide it by 100: 0.5 / 100 = 0.005.
Step 2: Calculate the interest amount.
- Add up the three components: the base interest rate of 10.2%, the 0.5 points (0.005), and the $200.
- Interest = 10.2% + 0.005 + $200
Step 3: Convert the interest into a decimal.
- Divide the interest amount by 100 to convert it to a decimal: 10.2% = 10.2 / 100 = 0.102.
Step 4: Calculate the interest on the loan amount.
- Multiply the loan amount of $70,000 by the decimal interest rate calculated in step 3: $70,000 * 0.102 = $7,140.
Step 5: Calculate the comparable interest rate.
- Divide the interest on the loan amount (from step 4) by the loan amount and multiply by 100 to get a percentage: ($7,140 / $70,000) * 100 = 10.2%.
Therefore, the comparable interest rate for the $70,000 loan with the given quote is 10.2%.