The Formula for Monthly Loan Payments

Oct 13, 2025 by wbrum.org 49 views

Understanding the Formula for Monthly Loan Payments

In this unit activity, we will delve into the world of saving and explore the concept of monthly loan payments. We will use a real-life scenario to illustrate the application of a mathematical formula, making it easier to understand and calculate the monthly loan payments.

The Formula for Monthly Loan Payments

The formula to compute the monthly loan payment is given by:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

M = monthly loan payment
P = principal loan amount (the amount borrowed)
i = monthly interest rate (annual interest rate divided by 12)
n = number of payments (the number of months the loan is for)

Isabel's Loan Scenario

Let's consider the scenario of Isabel, who wants to purchase a house. She makes a down payment of $5,000 and finances $16,950. The interest rate on her loan is 4.3% per annum. We need to calculate her monthly loan payment using the formula above.

Calculating the Monthly Loan Payment

First, we need to calculate the monthly interest rate (i). We can do this by dividing the annual interest rate by 12:

i = 4.3% / 12 = 0.003583

Next, we need to calculate the number of payments (n). Since Isabel is financing the loan for 30 years, we can calculate the number of payments as follows:

n = 30 years * 12 months/year = 360 months

Now, we can plug in the values into the formula:

M = 16950 [ 0.003583(1 + 0.003583)^360 ] / [ (1 + 0.003583)^360 – 1]

Solving for M

Using a calculator or a computer program, we can solve for M:

M ≈ $83.41

Therefore, Isabel's monthly loan payment is approximately $83.41.

Discussion Questions

What is the present value (PV) of the loan?
What is the monthly interest rate (i) in decimal form?
How many payments (n) will Isabel make on her loan?
What is the monthly loan payment (M) in decimal form?
What is the total amount Isabel will pay over the life of the loan?

Answer Key

The present value (PV) of the loan is $16,950.
The monthly interest rate (i) is 0.003583.
The number of payments (n) is 360.
The monthly loan payment (M) is $83.41.
The total amount Isabel will pay over the life of the loan is $30,000.

Conclusion

Understanding the Formula for Monthly Loan Payments

The Formula for Monthly Loan Payments

The formula to compute the monthly loan payment is given by:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

M = monthly loan payment
P = principal loan amount (the amount borrowed)
i = monthly interest rate (annual interest rate divided by 12)
n = number of payments (the number of months the loan is for)

Isabel's Loan Scenario

Calculating the Monthly Loan Payment

First, we need to calculate the monthly interest rate (i). We can do this by dividing the annual interest rate by 12:

i = 4.3% / 12 = 0.003583

Next, we need to calculate the number of payments (n). Since Isabel is financing the loan for 30 years, we can calculate the number of payments as follows:

n = 30 years * 12 months/year = 360 months

Now, we can plug in the values into the formula:

M = 16950 [ 0.003583(1 + 0.003583)^360 ] / [ (1 + 0.003583)^360 – 1]

Solving for M

Using a calculator or a computer program, we can solve for M:

M ≈ $83.41

Therefore, Isabel's monthly loan payment is approximately $83.41.

Discussion Questions

What is the present value (PV) of the loan?
What is the monthly interest rate (i) in decimal form?
How many payments (n) will Isabel make on her loan?
What is the monthly loan payment (M) in decimal form?
What is the total amount Isabel will pay over the life of the loan?

Answer Key

The present value (PV) of the loan is $16,950.
The monthly interest rate (i) is 0.003583.
The number of payments (n) is 360.
The monthly loan payment (M) is $83.41.
The total amount Isabel will pay over the life of the loan is $30,000.

Q&A Session

Q: What is the formula for calculating the monthly loan payment? A: The formula for calculating the monthly loan payment is given by:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Q: What is the present value (PV) of the loan? A: The present value (PV) of the loan is the amount borrowed, which is $16,950 in this case.

Q: What is the monthly interest rate (i) in decimal form? A: The monthly interest rate (i) is 0.003583 in decimal form.

Q: How many payments (n) will Isabel make on her loan? A: Isabel will make 360 payments on her loan, since she is financing the loan for 30 years.

Q: What is the monthly loan payment (M) in decimal form? A: The monthly loan payment (M) is $83.41 in decimal form.

Q: What is the total amount Isabel will pay over the life of the loan? A: The total amount Isabel will pay over the life of the loan is $30,000.

Q: What is the benefit of using the formula to calculate the monthly loan payment? A: The benefit of using the formula to calculate the monthly loan payment is that it allows you to determine the exact amount of the monthly payment, taking into account the interest rate and the number of payments.

Q: Can I use the formula to calculate the monthly loan payment for a loan with a variable interest rate? A: No, the formula is designed for loans with a fixed interest rate. If you have a loan with a variable interest rate, you will need to use a different formula or consult with a financial advisor.

Conclusion

In this unit activity, we have used the formula to compute Isabel's monthly loan payment. We have applied the formula to a real-life scenario, making it easier to understand and calculate the monthly loan payments. We have also discussed the concept of present value, monthly interest rate, and number of payments. By solving for M, we have found that Isabel's monthly loan payment is approximately $83.41.