Question
Find the monthly payment needed to amortize principal and
interest for the following fixed-rate mortgage.
Mortgage amount:
Term of mortgage: 25 years
Interest rate:
interest for the following fixed-rate mortgage.
Mortgage amount:
Term of mortgage: 25 years
Interest rate:
Ask by Sullivan Munoz. in the United States
Dec 06,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The monthly payment for the mortgage is approximately $1,039.36.
Solution
To calculate the monthly payment for a fixed-rate mortgage, we can use the formula for the monthly payment
where:
-
= monthly payment -
= principal loan amount (mortgage amount) -
= monthly interest rate (annual interest rate divided by 12) -
= number of payments (loan term in months)
Given:
-
- Annual interest rate =
or - Term of mortgage = 25 years
First, we need to convert the annual interest rate to a monthly interest rate and calculate the total number of payments:
- Calculate the monthly interest rate
:
- Calculate the total number of payments
:
Now we can substitute these values into the monthly payment formula:
Calculating
Now substituting this back into the formula:
Calculating the numerator and denominator:
Now substituting these values into the formula:
Thus, the monthly payment needed to amortize the principal and interest for the mortgage is approximately:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To calculate the monthly payment for a fixed-rate mortgage, you can use the formula:
where:
-
is the total monthly mortgage payment, -
is the loan amount ($110,300), -
is the monthly interest rate (annual rate divided by 12), and -
is the number of payments (loan term in months).
Given an interest rate of
Plugging these numbers into the formula, we get:
Calculating this will yield the monthly payment, which is approximately
Did you know that the mortgage system as we know it today has its origins back in the Middle Ages, primarily in England? The term “mortgage” comes from the Old French word “mort” meaning “dead,” and “gage” meaning “pledge.” This referred to the pledge ending (or “dying”) when the debt is paid off or the property is taken back by the lender if the borrower defaults.
In today’s world, understanding mortgage payments can help you budget effectively. Remember, when planning a mortgage, don’t forget about other costs such as property taxes, homeowner’s insurance, and potential homeowners association (HOA) fees. These can significantly impact your monthly budget! It’s also wise to consider shopping around for the best mortgage rates, as even a small difference can lead to massive savings over the life of the loan.
