Answer:
$334.02
Explanation:
To calculate the monthly payment for a 30-year fixed-rate mortgage, we can use the formula for the monthly payment of a fixed-rate mortgage:
�
=
�
⋅
�
⋅
(
1
+
�
)
�
(
1
+
�
)
�
−
1
M=
(1+r)
n
−1
P⋅r⋅(1+r)
n
where:
�
M is the monthly payment.
�
P is the principal amount of the loan (mortgage amount after the down payment), which is $270,000 in this case.
�
r is the monthly interest rate, which is the annual interest rate divided by 12 (since there are 12 months in a year). The annual interest rate is 6%, so the monthly interest rate is
6
100
×
12
100×12
6
.
�
n is the total number of monthly payments, which is the number of years multiplied by 12 (since there are 12 months in a year). In this case, it is
30
×
12
30×12.
Now, let's plug in the values and calculate the monthly payment:
�
=
270
,
000
×
0.06
12
×
(
1
+
0.06
12
)
30
×
12
(
1
+
0.06
12
)
30
×
12
−
1
M=
(1+
12
0.06
)
30×12
−1
270,000×
12
0.06
×(1+
12
0.06
)
30×12
�
=
270
,
000
×
0.005
×
(
1
+
0.005
)
360
(
1
+
0.005
)
360
−
1
M=
(1+0.005)
360
−1
270,000×0.005×(1+0.005)
360
Now, perform the calculations inside the parentheses:
�
=
270
,
000
×
0.005
×
5.1167
5.1167
−
1
M=
5.1167−1
270,000×0.005×5.1167
�
=
1
,
375.5025
4.1167
M=
4.1167
1,375.5025
�
≈
334.02
M≈334.02
The monthly payment, excluding escrow taxes and insurance, is approximately $334.02 when rounded to the nearest cent.