Since question a has been answered, lets try to answer question b directly.
To answer question b, let's calculate the amount of interest Rob would expect to pay in the first month on her loan. We will use the monthly interest rate and apply it to the principal loan amount.
First, we translate the annual percentage rate (APR) into a monthly interest rate. Since APR is given in terms of an annual rate, we divide it by 12 (the number of months in a year) to get the monthly interest rate.
APR = 6.21%
Monthly interest rate = APR / 12
Let's convert the APR to a decimal and then calculate the monthly interest rate:
Annual rate (in decimal form) = 6.21 / 100 = 0.0621
Monthly interest rate = 0.0621 / 12
Calculating the monthly interest rate gives us:
Monthly interest rate = 0.0621 / 12 ≈ 0.005175
We then calculate the interest payment for the first month by multiplying the monthly interest rate by the principal amount.
First month's interest = Principal loan amount × Monthly interest rate
We can now calculate it using the given principal amount:
First month's interest = $490,000 × 0.005175 ≈ $2,535.75
So, in the first month, Rob would expect to pay approximately $2,535.75 in interest.
To answer question c, which you correctly stated involves subtracting the first month's interest from the total monthly payment to find out how much will go toward the principal, we can use the already known monthly payment value:
c. Monthly payment (as provided) = $3220.28
First month's interest (as just calculated) = $2,535.75
Principal in the first month = Monthly payment - First month's interest
Principal in the first month = $3220.28 - $2,535.75 ≈ $684.53
So, Rob's first monthly payment will consist of approximately $684.53 going toward the principal and the rest covering the interest.
