Final answer:
Cassidy's monthly payment for the financed portion of the house after a 10% down payment on a $285,000 property at a 4% interest rate for 30 years is approximately $1,225.30.
Step-by-step explanation:
To calculate the monthly payment Cassidy has to make for the financed portion of the house, we'll use the formula for a fixed-rate mortgage. Cassidy's down payment is 10% of the $285,000 house, so that is $28,500, leaving a balance of $256,500 to be financed. The annual interest rate is 4%, which we'll convert to a monthly rate by dividing by 12. The terms of the loan are for 30 years, which equates to 360 monthly payments.
We can use the formula for a fixed-rate mortgage:
P = L[c(1 + c)^n] / [(1 + c)^n - 1]
Where:
- P is the monthly payment
- L is the loan amount ($256,500)
- c is the monthly interest rate (4% annually divided by 12 months)
- n is the number of payments (360)
Calculating the monthly interest rate c gives us:
c = 4% / 12 = 0.004
Now we can calculate the monthly payment P:
P = $256,500[0.004(1 + 0.004)^360] / [(1 + 0.004)^360 - 1]
Using a calculator, we find that the monthly payment P is approximately $1,225.30.
Therefore, Cassidy's monthly payment for the house will be about $1,225.30.