Final answer:
To find Raymond's new mortgage payment, we use the annuity formula with the remaining balance, extended term, and reduced interest rate to calculate a new monthly payment of approximately $815.09, which is answer option (a).
Step-by-step explanation:
To calculate Raymond's new mortgage payment after the loan extension and interest rate reduction, we need to use the formula for an annuity, which is commonly used to calculate mortgage payments. The new loan term will be 37 years (30 original years plus 7 additional years), and the remaining loan balance is $170,118.49 with a new annual interest rate of 4.05%. We break down the interest rate to a monthly rate by dividing by 12.
To find the monthly payment, the formula is as follows:
P = (Pv * r) / (1 - (1 + r)^-n)
Where:
- P is the monthly payment
- Pv is the present value of the loan, which is $170,118.49
- r is the monthly interest rate (annual rate / 12)
- n is the total number of payments (loan term in years * 12)
First, calculate the monthly interest rate:
r = 4.05% / 12 = 0.3375%
Convert the percentage to decimal:
r = 0.3375 / 100 = 0.003375
Now, calculate n:
n = 37 years * 12 months/year = 444 months
With these values, we can calculate the monthly payment (P):
P = ($170,118.49 * 0.003375) / (1 - (1 + 0.003375)^-444)
Upon calculation, we find that:
P ≈ $815.09
Therefore, Raymond's new monthly mortgage payment would be approximately $815.09, fitting answer choice (a).