https://file.aiquickdraw.com/mathbot/file/17276424328703t8hh4hy.jpg

The formula in the image appears to be for calculating the monthly payment $ M $ for a loan, typically used in finance to determine mortgage or loan repayments. The formula is given as:

\[
M = \frac{P \left( \frac{r}{12} \right)}{1 - \left(1 + \frac{r}{12}\right)^{-12t}}
\]

where:
- $ P $ is the principal loan amount,
- $ r $ is the annual interest rate,
- $ t $ is the loan term in years.

In this particular formula:
- $ P = 20,013.68 $,
- $ r = 0.048 $ (4.8% annual interest rate),
- and $ t = 10 $ years.

The formula calculates to approximately $ M = 210.325 $, which represents the monthly payment for a 10-year loan with the given parameters.

### Would you like a detailed breakdown of the calculation?

#### Related Questions:
1. How would the monthly payment change if the loan term was increased to 15 years?
2. What happens to the monthly payment if the interest rate is reduced to 4%?
3. How does changing the principal amount affect the monthly payment?
4. Can you explain the formula derivation in detail?
5. What if the payments were made quarterly instead of monthly?

**Tip:** Understanding the time value of money is crucial when dealing with loans, as small changes in the interest rate or loan term can significantly affect the monthly payments.

Calculate the monthly payment for a loan using the given formula with a principal amount of $20,013.68, an annual interest rate of 4.8%, and a loan term of 10 years.

Learn how to calculate the monthly payment for a loan with a principal amount of $20,013.68, an annual interest rate of 4.8%, and a 10-year term. The formula involves algebra and exponential functions, making it suitable for students in Grades 11-12 and above.

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