Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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![### Calculating Monthly Mortgage Payment
The formula for calculating the monthly mortgage payment \( M \) is given by:
\[
M = 1500 \cdot \frac{\left(\frac{0.0375}{12}\right) \cdot \left(1 + \frac{0.0375}{12}\right)^{15}}{\left(1 + \frac{0.0275}{12}\right) - 1}
\]
In this formula:
- \( M \) is the monthly mortgage payment.
- The constant 1500 represents the principal amount of the loan.
- The term \( \frac{0.0375}{12} \) is the monthly interest rate (3.75% annual interest rate divided by 12).
- \( \left(1 + \frac{0.0375}{12}\right)^{15} \) is the compound interest component where 15 represents the number of periods.
- The denominator \( \left(1 + \frac{0.0275}{12}\right) - 1 \) also relates to the interest rate adjusted for monthly computation.
**Steps to calculate:**
1. Convert the annual interest rate to a monthly rate: \(\frac{0.0375}{12}\).
2. Calculate the compound interest term: \( \left(1 + \frac{0.0375}{12}\right)^{15} \).
3. Determine the denominator's value: \(\left(1 + \frac{0.0275}{12}\right) - 1\).
4. Combine these components to find the monthly mortgage payment \( M \).
This formula allows borrowers to understand how much they will need to pay each month to repay their mortgage over the specified term while considering the interest accrued throughout the period. Understanding this calculation is critical for financial planning in the home-buying process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9434212-c4f7-4fee-ac22-2926cb5e8f10%2Fe86326c4-307a-4109-8e57-13aaf2676134%2Fe4ql6pd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Monthly Mortgage Payment
The formula for calculating the monthly mortgage payment \( M \) is given by:
\[
M = 1500 \cdot \frac{\left(\frac{0.0375}{12}\right) \cdot \left(1 + \frac{0.0375}{12}\right)^{15}}{\left(1 + \frac{0.0275}{12}\right) - 1}
\]
In this formula:
- \( M \) is the monthly mortgage payment.
- The constant 1500 represents the principal amount of the loan.
- The term \( \frac{0.0375}{12} \) is the monthly interest rate (3.75% annual interest rate divided by 12).
- \( \left(1 + \frac{0.0375}{12}\right)^{15} \) is the compound interest component where 15 represents the number of periods.
- The denominator \( \left(1 + \frac{0.0275}{12}\right) - 1 \) also relates to the interest rate adjusted for monthly computation.
**Steps to calculate:**
1. Convert the annual interest rate to a monthly rate: \(\frac{0.0375}{12}\).
2. Calculate the compound interest term: \( \left(1 + \frac{0.0375}{12}\right)^{15} \).
3. Determine the denominator's value: \(\left(1 + \frac{0.0275}{12}\right) - 1\).
4. Combine these components to find the monthly mortgage payment \( M \).
This formula allows borrowers to understand how much they will need to pay each month to repay their mortgage over the specified term while considering the interest accrued throughout the period. Understanding this calculation is critical for financial planning in the home-buying process.
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