0.0375 15 1(1+ 0.0375 12 12 M=1500. 0.0275 1 + -1 12

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
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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