Matthew obtains a 30-year $81,000 house loan with APR of 8.08%. What is his monthly payment?
monthly rate = .0808/12 = .0067333..
81000 = x( 1 - 1.0067333..^-360)/.00673333..
...
...
x = 598.87
To calculate Matthew's monthly payment, we can use the formula for monthly mortgage payments. The formula is:
M = P[r(1+r)^n]/[(1+r)^n-1]
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n = total number of payments (number of years multiplied by 12)
Let's substitute the given values into the formula:
P = $81,000
APR = 8.08% = 0.0808
r = 0.0808/12 = 0.0067333 (rounded to 6 decimal places)
n = 30 years * 12 months/year = 360 months
M = $81,000 [0.0067333(1+0.0067333)^360] / [(1+0.0067333)^360-1]
Now we can calculate it step by step:
First, calculate the term in the square bracket:
(1+0.0067333)^360 = 751.6117 (rounded to 4 decimal places)
Next, calculate the term in the denominator:
[(1+0.0067333)^360-1] = 750.6117 (rounded to 4 decimal places)
Now, substitute the values back into the formula:
M = $81,000 [0.0067333(751.6117)] / 750.6117
Next, solve the multiplication inside the bracket:
0.0067333 * 751.6117 = 5.0563 (rounded to 4 decimal places)
Finally, calculate the monthly payment:
M = $81,000 * 5.0563 / 750.6117
M = $545.4290 (rounded to 2 decimal places)
So Matthew's monthly payment for the $81,000 house loan with an APR of 8.08% is approximately $545.43.
To calculate Matthew's monthly payment for the house loan, we can use the formula for calculating the monthly payment on a fixed-rate mortgage. The formula is:
M = P * (r * (1+r)^n) / ((1+r)^n - 1)
Where:
M is the monthly payment
P is the loan amount ($81,000 in this case)
r is the monthly interest rate (APR divided by 12)
n is the total number of monthly payments (30 years multiplied by 12 months)
First, let's calculate the monthly interest rate. The APR is 8.08%, so the monthly interest rate would be (8.08 / 100) / 12 = 0.0067333.
Next, let's calculate the total number of monthly payments. 30 years multiplied by 12 months gives us 360 total monthly payments.
Now we can plug these values into the formula:
M = 81,000 * (0.0067333 * (1+0.0067333)^360) / ((1+0.0067333)^360 -1)
By solving this equation, we can find Matthew's monthly payment for the house loan.