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The price of a home is $300,000. After a 10% down payment, the mortgage is $270,000. If this is financed with a 30-year fixed-rate mortgage at 6%, what is the monthly payment, excluding escrow taxes and insurance?

Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer.

1 Answer

3 votes

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.

User Shaun Scovil
by
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