Find the following for a $200,000 fixed-rate mortgage and the given information.
a) Monthly mortgage payment (principal and interest)
b) Monthly house payment (including property taxes and insurance)
c) Initial monthly interest
d) Income tax deductible portion of initial house payment
e) Net initial monthly cost for the home (considering tax savings)
Term of Mortgage
Interest Rate
Annual Property Tax
Annual Insurance
Owner's Income Tax Bracket
20 years
6.5%
$900
$492
35%
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Part 1
a) The monthly mortgage payment is $enter your response here.
(Round to the nearest dollar as needed.)
To calculate the monthly mortgage payment, we can use the formula for a fixed-rate mortgage:
M = P * r * (1 + r)^n / ((1 + r)^n - 1),
where M is the monthly mortgage payment, P is the principal loan amount, r is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of monthly payments.
Given:
Principal loan amount (P) = $200,000
Annual interest rate = 6.5%
Term of mortgage (n) = 20 years = 20 * 12 = 240 months
First, let's calculate the monthly interest rate:
Monthly interest rate (r) = 6.5% / 12 = 0.065 / 12 = 0.0054167
Now, calculate the monthly mortgage payment:
M = $200,000 * 0.0054167 * (1 + 0.0054167)^240 / ((1 + 0.0054167)^240 - 1)
M ≈ $1,264
Therefore, the monthly mortgage payment is approximately $1,264.
To calculate the monthly mortgage payment (principal and interest) for a $200,000 fixed-rate mortgage, we'll need the term of the mortgage, the interest rate, and the loan amount.
Term of Mortgage: 20 years
Interest Rate: 6.5%
Using these values, we can calculate the monthly mortgage payment using the formula for a fixed-rate mortgage:
M = P * [(r * (1 + r)^n) / ((1 + r)^n - 1)]
Where:
M = Monthly mortgage payment
P = Loan amount = $200,000
r = Monthly interest rate = (Annual interest rate / 12) = (6.5% / 100 / 12)
n = Total number of payments = (Term of mortgage in years * 12)
Substituting in the values, we get:
M = $200,000 * [(0.065 / 12) * (1 + (0.065 / 12))^(20 * 12)] / [(1 + (0.065 / 12))^(20 * 12) - 1]
Using a calculator to evaluate the expression, we find:
M ≈ $1,411.10
Therefore, the monthly mortgage payment (principal and interest) for the given information is approximately $1,411.
To calculate the monthly mortgage payment, we can use the formula for calculating the monthly payment on a fixed-rate mortgage:
Monthly Payment = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
P = Principal amount of the mortgage ($200,000)
r = Monthly interest rate (6.5% / 12 months = 0.0054, since the interest rate is given as an annual rate)
n = Total number of monthly payments (20 years * 12 months = 240)
Plugging in the values, we get:
Monthly Payment = 200000 * (0.0054(1+0.0054)^240) / ((1+0.0054)^240 - 1)
Calculating this equation will give you the monthly mortgage payment.