Find \[$ C \$\], The Total Of The Payments, And The Monthly Payment. Choose The Correct Answers.$\[ \operatorname{Interest}(I)=\frac{2yc}{m(n+1)} \\]Sue Stitch Buys A Sewing Machine. The Price, Including Tax, Is \$575.00. She

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Understanding the Problem

When it comes to calculating the total of payments and the monthly payment for a loan or a purchase, it's essential to understand the formula and the variables involved. In this article, we will delve into the world of mathematics and explore how to find the total of payments and the monthly payment using the given formula.

The Formula: Interest (I) = 2yc / m(n+1)

The formula provided is:

Interest⁡(I)=2ycm(n+1){ \operatorname{Interest}(I)=\frac{2yc}{m(n+1)} }

Where:

  • I = Interest
  • y = Annual interest rate
  • c = Total cost of the item (including tax)
  • m = Monthly payment
  • n = Number of payments

Breaking Down the Formula

To find the total of payments and the monthly payment, we need to break down the formula and understand each variable. The annual interest rate (y) is a percentage that represents the interest charged on the loan or purchase per year. The total cost of the item (c) includes the price of the item plus tax. The monthly payment (m) is the amount paid each month, and the number of payments (n) is the total number of payments made over the life of the loan or purchase.

Finding the Total of Payments

To find the total of payments, we need to multiply the monthly payment (m) by the number of payments (n). This will give us the total amount paid over the life of the loan or purchase.

Finding the Monthly Payment

To find the monthly payment, we need to use the formula provided. We can rearrange the formula to solve for m:

m=2ycn(n+1){ m = \frac{2yc}{n(n+1)} }

Example: Sue Stitch's Sewing Machine

Let's use Sue Stitch's sewing machine purchase as an example. The price of the sewing machine, including tax, is $575.00. We are given the annual interest rate (y) as 10% and the number of payments (n) as 12.

Step 1: Plug in the Values

First, we need to plug in the values into the formula:

m=2(0.10)(575)12(12+1){ m = \frac{2(0.10)(575)}{12(12+1)} }

Step 2: Simplify the Equation

Next, we need to simplify the equation:

m=115156{ m = \frac{115}{156} }

Step 3: Calculate the Monthly Payment

Now, we can calculate the monthly payment:

m=0.7372{ m = 0.7372 }

Step 4: Find the Total of Payments

To find the total of payments, we need to multiply the monthly payment (m) by the number of payments (n):

Total of Payments=m×n{ \text{Total of Payments} = m \times n }

Step 5: Calculate the Total of Payments

Now, we can calculate the total of payments:

Total of Payments=0.7372×12{ \text{Total of Payments} = 0.7372 \times 12 }

Step 6: Calculate the Total of Payments

Now, we can calculate the total of payments:

Total of Payments=8.8454{ \text{Total of Payments} = 8.8454 }

Conclusion

In conclusion, finding the total of payments and the monthly payment requires a clear understanding of the formula and the variables involved. By breaking down the formula and using the given values, we can calculate the total of payments and the monthly payment. In this article, we used Sue Stitch's sewing machine purchase as an example to illustrate the steps involved in finding the total of payments and the monthly payment.

Key Takeaways

  • The formula for finding the interest (I) is: I = 2yc / m(n+1)
  • The formula for finding the monthly payment (m) is: m = 2yc / n(n+1)
  • To find the total of payments, multiply the monthly payment (m) by the number of payments (n)
  • Use the given values and plug them into the formula to calculate the monthly payment and the total of payments.

Final Answer

The final answer is:

  • Monthly payment: $0.7372
  • Total of payments: $8.8454

Q: What is the formula for finding the interest (I)?

A: The formula for finding the interest (I) is:

Interest⁡(I)=2ycm(n+1){ \operatorname{Interest}(I)=\frac{2yc}{m(n+1)} }

Where:

  • I = Interest
  • y = Annual interest rate
  • c = Total cost of the item (including tax)
  • m = Monthly payment
  • n = Number of payments

Q: How do I find the monthly payment (m)?

A: To find the monthly payment (m), you can use the formula:

m=2ycn(n+1){ m = \frac{2yc}{n(n+1)} }

Q: What is the total of payments?

A: The total of payments is the sum of all the monthly payments made over the life of the loan or purchase. To find the total of payments, multiply the monthly payment (m) by the number of payments (n).

Q: How do I calculate the total of payments?

A: To calculate the total of payments, follow these steps:

  1. Plug in the values into the formula: m = 2yc / n(n+1)
  2. Simplify the equation
  3. Calculate the monthly payment (m)
  4. Multiply the monthly payment (m) by the number of payments (n)

Q: What is the annual interest rate (y)?

A: The annual interest rate (y) is a percentage that represents the interest charged on the loan or purchase per year.

Q: What is the total cost of the item (c)?

A: The total cost of the item (c) includes the price of the item plus tax.

Q: What is the number of payments (n)?

A: The number of payments (n) is the total number of payments made over the life of the loan or purchase.

Q: How do I use the formula to find the total of payments and the monthly payment?

A: To use the formula, follow these steps:

  1. Plug in the values into the formula: I = 2yc / m(n+1)
  2. Simplify the equation
  3. Calculate the interest (I)
  4. Use the formula to find the monthly payment (m)
  5. Multiply the monthly payment (m) by the number of payments (n) to find the total of payments

Q: What if I have a different interest rate or number of payments?

A: If you have a different interest rate or number of payments, simply plug in the new values into the formula and recalculate the monthly payment and the total of payments.

Q: Can I use this formula for any type of loan or purchase?

A: Yes, this formula can be used for any type of loan or purchase, including car loans, mortgages, and personal loans.

Q: How accurate is this formula?

A: This formula is an estimate and may not be 100% accurate. However, it can provide a good estimate of the monthly payment and the total of payments.

Q: Can I use a calculator to find the monthly payment and the total of payments?

A: Yes, you can use a calculator to find the monthly payment and the total of payments. Simply plug in the values and the calculator will do the rest.

Q: What if I have a variable interest rate?

A: If you have a variable interest rate, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a balloon payment?

A: No, this formula is not suitable for a loan with a balloon payment. You will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: What if I have a loan with a prepayment penalty?

A: If you have a loan with a prepayment penalty, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a variable payment schedule?

A: No, this formula is not suitable for a loan with a variable payment schedule. You will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: What if I have a loan with a deferred payment?

A: If you have a loan with a deferred payment, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a co-signer?

A: Yes, you can use this formula for a loan with a co-signer. However, you will need to take into account the co-signer's credit score and income when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a co-borrower?

A: If you have a loan with a co-borrower, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a credit union?

A: Yes, you can use this formula for a loan with a credit union. However, you will need to take into account the credit union's interest rate and fees when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a bank?

A: If you have a loan with a bank, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a mortgage broker?

A: Yes, you can use this formula for a loan with a mortgage broker. However, you will need to take into account the mortgage broker's fees and commissions when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a mortgage lender?

A: If you have a loan with a mortgage lender, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a home equity loan?

A: Yes, you can use this formula for a loan with a home equity loan. However, you will need to take into account the home equity loan's interest rate and fees when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a home equity line of credit?

A: If you have a loan with a home equity line of credit, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a personal loan?

A: Yes, you can use this formula for a loan with a personal loan. However, you will need to take into account the personal loan's interest rate and fees when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a student loan?

A: If you have a loan with a student loan, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a business loan?

A: Yes, you can use this formula for a loan with a business loan. However, you will need to take into account the business loan's interest rate and fees when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a commercial loan?

A: If you have a loan with a commercial loan, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a construction loan?

A: Yes, you can use this formula for a loan with a construction loan. However, you will need to take into account the construction loan's interest rate and fees when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a land loan?

A: If you have a loan with a land loan, you will need to use a different formula to find the monthly payment and the total of payments. Consult with a financial advisor or use a financial calculator to determine the correct formula.

Q: Can I use this formula for a loan with a mobile home loan?

A: Yes, you can use this formula for a loan with a mobile home loan. However, you will need to take into account the mobile home loan's interest rate and fees when calculating the monthly payment and the total of payments.

Q: What if I have a loan with a manufactured home loan?

A: If you have a loan with a manufactured home loan, you will need to use a different formula to find the monthly payment and the total of payments.