Describe The Effect An Increase In \[$ N \$\], The Number Of Payment Periods, Has On The Monthly Payment \[$ P \$\] In The Formula:$\[ P = PV \cdot \frac{1}{1 - (1 + I)^{-\pi}} \\]a. An Increase In \[$ N \$\], The

Understanding the Formula

The formula for calculating monthly payments is given by:

${ P = PV \cdot \frac{1}{1 - (1 + i)^{-n}} }$

where:

• $P$ is the monthly payment
• $PV$ is the present value (the initial amount borrowed)
• $i$ is the monthly interest rate (annual interest rate divided by 12)
• $n$ is the number of payment periods (the number of months the loan is repaid over)

The Effect of Increasing Payment Periods

In this section, we will explore the effect of increasing the number of payment periods ($n$) on the monthly payment ($P$).

An Increase in $n$

When the number of payment periods ($n$) increases, the monthly payment ($P$) decreases. This is because the formula for calculating monthly payments includes the term $(1 + i)^{-n}$, which decreases as $n$ increases.

To understand why this is the case, let's consider the following:

• When $n$ is small, the term $(1 + i)^{-n}$ is close to 1, and the formula for calculating monthly payments is approximately:

${ P \approx PV \cdot \frac{1}{1 - (1 + i)} }$

• As $n$ increases, the term $(1 + i)^{-n}$ decreases, and the formula for calculating monthly payments becomes:

${ P \approx PV \cdot \frac{1}{1 - (1 + i)^{-n}} }$

• When $n$ is large, the term $(1 + i)^{-n}$ is close to 0, and the formula for calculating monthly payments is approximately:

${ P \approx PV \cdot \frac{1}{1} }$

This means that as the number of payment periods ($n$) increases, the monthly payment ($P$) decreases.

The Relationship Between $n$ and $P$

To better understand the relationship between $n$ and $P$, let's consider the following:

• When $n$ is small, the monthly payment ($P$) is high.
• As $n$ increases, the monthly payment ($P$) decreases.
• When $n$ is large, the monthly payment ($P$) is low.

This relationship can be seen in the following graph:

$n$	$P$
12	100
24	80
36	60
48	40
60	20

As we can see, as the number of payment periods ($n$) increases, the monthly payment ($P$) decreases.

The Impact on Loan Repayment

The effect of increasing payment periods on monthly payments has a significant impact on loan repayment.

• When the number of payment periods ($n$) is small, the monthly payment ($P$) is high, and the loan is repaid quickly.
• As the number of payment periods ($n$) increases, the monthly payment ($P$) decreases, and the loan is repaid over a longer period.

This means that borrowers who take out loans with longer repayment periods may end up paying more in interest over the life of the loan.

Conclusion

In conclusion, increasing the number of payment periods ($n$) has a significant impact on the monthly payment ($P$). As $n$ increases, $P$ decreases. This means that borrowers who take out loans with longer repayment periods may end up paying more in interest over the life of the loan.

References

• [1] Investopedia. (2022). How to Calculate Monthly Payments.
• [2] Bankrate. (2022). How to Calculate Loan Payments.
• [3] NerdWallet. (2022). How to Calculate Loan Payments.

Additional Resources

• [1] Calculator for calculating monthly payments.
• [2] Formula for calculating monthly payments.
• [3] Guide to loan repayment.
  Frequently Asked Questions About the Impact of Increasing Payment Periods on Monthly Payments =============================================================================================

Q: What is the formula for calculating monthly payments?

A: The formula for calculating monthly payments is given by:

${ P = PV \cdot \frac{1}{1 - (1 + i)^{-n}} }$

where:

• $P$ is the monthly payment
• $PV$ is the present value (the initial amount borrowed)
• $i$ is the monthly interest rate (annual interest rate divided by 12)
• $n$ is the number of payment periods (the number of months the loan is repaid over)

Q: What happens to the monthly payment when the number of payment periods increases?

A: When the number of payment periods ($n$) increases, the monthly payment ($P$) decreases. This is because the formula for calculating monthly payments includes the term $(1 + i)^{-n}$, which decreases as $n$ increases.

Q: Why does the monthly payment decrease when the number of payment periods increases?

A: The monthly payment decreases when the number of payment periods increases because the term $(1 + i)^{-n}$ in the formula for calculating monthly payments decreases as $n$ increases. This means that the loan is repaid over a longer period, and the monthly payment is lower.

Q: What is the relationship between the number of payment periods and the monthly payment?

A: The relationship between the number of payment periods ($n$) and the monthly payment ($P$) is as follows:

• When $n$ is small, the monthly payment ($P$) is high.
• As $n$ increases, the monthly payment ($P$) decreases.
• When $n$ is large, the monthly payment ($P$) is low.

Q: How does the impact of increasing payment periods on monthly payments affect loan repayment?

A: The impact of increasing payment periods on monthly payments has a significant impact on loan repayment. When the number of payment periods ($n$) is small, the monthly payment ($P$) is high, and the loan is repaid quickly. As the number of payment periods ($n$) increases, the monthly payment ($P$) decreases, and the loan is repaid over a longer period.

Q: What are the implications of increasing payment periods on monthly payments for borrowers?

A: The implications of increasing payment periods on monthly payments for borrowers are as follows:

• Borrowers who take out loans with longer repayment periods may end up paying more in interest over the life of the loan.
• Borrowers who take out loans with shorter repayment periods may end up paying less in interest over the life of the loan.

Q: How can borrowers minimize the impact of increasing payment periods on monthly payments?

A: Borrowers can minimize the impact of increasing payment periods on monthly payments by:

• Taking out loans with shorter repayment periods.
• Making extra payments towards the loan principal.
• Considering alternative loan options with lower interest rates.

Q: What are some common mistakes borrowers make when it comes to increasing payment periods on monthly payments?

A: Some common mistakes borrowers make when it comes to increasing payment periods on monthly payments are:

• Not understanding the impact of increasing payment periods on monthly payments.
• Not considering alternative loan options with lower interest rates.
• Not making extra payments towards the loan principal.

Q: How can borrowers avoid these mistakes and make informed decisions about increasing payment periods on monthly payments?

A: Borrowers can avoid these mistakes and make informed decisions about increasing payment periods on monthly payments by:

• Educating themselves about the impact of increasing payment periods on monthly payments.
• Considering alternative loan options with lower interest rates.
• Making extra payments towards the loan principal.

Q: What are some resources available to borrowers who want to learn more about increasing payment periods on monthly payments?

A: Some resources available to borrowers who want to learn more about increasing payment periods on monthly payments are:

• Online calculators for calculating monthly payments.
• Formula for calculating monthly payments.
• Guides to loan repayment.

Q: How can borrowers get help if they are struggling to make their monthly payments?

A: Borrowers who are struggling to make their monthly payments can get help by:

• Contacting their lender to discuss options for modifying their loan.
• Seeking the advice of a financial advisor.
• Considering debt consolidation or credit counseling services.