Final answer:
Carrie's monthly payment is approximately $1,389.11, while Joe's monthly payment in the first month is approximately $916.67 assuming it's interest-only. Carrie's monthly payment will remain constant over time, but Joe's monthly payment may change due to the adjustable interest rate.
Step-by-step explanation:
To calculate the monthly payment for Carrie's mortgage, we can use the formula for the monthly payment of a fixed-rate mortgage:
Monthly payment = P * (r/12) * (1+r/12)^n / ((1+r/12)^n-1)
Where:
P = principal amount of the loan ($220,000)
r = annual interest rate (6.5%, which is equivalent to 0.065)
n = number of payments (30 years, which is equivalent to 360 months)
Substituting these values into the formula, we get:
Monthly payment = 220,000 * (0.065/12) * (1+0.065/12)^360 / ((1+0.065/12)^360-1)
Calculating this expression gives us a monthly payment of approximately $1,389.11.
For Joe's mortgage in the first month, assuming it's interest-only, the monthly payment would be calculated by multiplying the principal amount by the interest rate:
Monthly payment = P * (r/12)
Substituting the values for Joe's mortgage into the formula, we get:
Monthly payment = 220,000 * (0.055/12)
Calculating this expression gives us a monthly payment of approximately $916.67.
Over time, Carrie's monthly payment will remain constant because she has a fixed-rate mortgage. On the other hand, Joe's monthly payment will change over time because he has an adjustable-rate mortgage. The interest rate for an adjustable-rate mortgage can change periodically based on market conditions. This means that Joe's monthly payment could increase or decrease depending on how the interest rate changes.