Final answer:
To calculate Ramona's monthly mortgage payment of a $200,000 loan at a 3.7% annual interest rate compounded monthly over 20 years, use the fixed-rate mortgage formula. It results in a monthly payment of approximately $1,168.30.
Step-by-step explanation:
To calculate the monthly payment for Ramona's mortgage, we can use the formula for the monthly payment of a fixed-rate mortgage, which is derived from the present value of an annuity formula:
M = P \frac{r(1+r)^n}{(1+r)^n-1}
Where:
- M is the total monthly mortgage payment.
- P is the principal loan amount ($200,000).
- r is the monthly interest rate (annual rate divided by 12).
- n is the number of payments (loan term in years multiplied by 12).
First, convert the annual rate to a monthly rate:
r = 3.7% / 12 = 0.00308333 (approximated)
Then calculate n:
n = 20 years * 12 months/year = 240 months
Now we can plug the values into the formula:
M = $200,000 \frac{(0.00308333)(1+0.00308333)^{240}}{(1+0.00308333)^{240}-1}
Finally, calculate the monthly payment:
M = $200,000 \frac{(0.00308333)(1.00308333)^{240}}{(1.00308333)^{240}-1} = $1,168.30 (approximated)
Ramona's monthly payment will be approximately $1,168.30.