Suzanne Has Purchased A Car With A List Price Of $$23,860$. She Traded In Her Previous Car, Which Was A Dodge In Good Condition, And Financed The Rest Of The Cost For Five Years At A Rate Of $11.62%$$, Compounded Monthly.

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Introduction

In this article, we will delve into the world of mathematics and explore the concept of compound interest. Suzanne, a car buyer, has purchased a vehicle with a list price of $23,860. She has traded in her previous car and financed the remaining cost for five years at a rate of 11.62%, compounded monthly. We will use mathematical formulas to calculate the total amount Suzanne will pay over the five-year period.

The Formula for Compound Interest

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

Where:

  • A is the amount of money accumulated after n years, including interest
  • P is the principal amount (the initial amount of money)
  • r is the annual interest rate (in decimal form)
  • n is the number of times that interest is compounded per year
  • t is the time the money is invested for, in years

Calculating the Total Amount

In this case, Suzanne has financed the remaining cost of the car, which is $23,860. The interest rate is 11.62%, compounded monthly. We will use the formula above to calculate the total amount Suzanne will pay over the five-year period.

First, we need to convert the annual interest rate to a decimal form:

r = 11.62% = 0.1162

Since the interest is compounded monthly, we will use n = 12.

The principal amount (P) is the remaining cost of the car, which is $23,860.

The time period (t) is five years.

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

A = 23860(1 + 0.1162/12)^(12*5)

Using a Calculator to Find the Total Amount

To find the total amount, we can use a calculator to evaluate the expression above:

A ≈ 38,419.19

So, the total amount Suzanne will pay over the five-year period is approximately $38,419.19.

Breaking Down the Total Amount

To understand how the total amount is calculated, let's break it down into its components.

The total amount is made up of the principal amount (P) and the interest accrued over the five-year period.

The interest accrued can be calculated using the formula:

Interest = P(1 + r/n)^(nt) - P

Plugging in the values, we get:

Interest ≈ 14,559.19

So, the interest accrued over the five-year period is approximately $14,559.19.

The Effect of Compounding

The formula for compound interest shows that the interest is compounded monthly. This means that the interest is applied to the principal amount at the end of each month.

To illustrate the effect of compounding, let's consider an example.

Suppose Suzanne had financed the remaining cost of the car for one year at the same interest rate of 11.62%, compounded monthly.

The total amount she would pay over the one-year period would be:

A = 23860(1 + 0.1162/12)^(12*1)

A ≈ 25,419.19

So, the total amount Suzanne would pay over the one-year period is approximately $25,419..

Conclusion

In this article, we have used mathematical formulas to calculate the total amount Suzanne will pay over the five-year period. We have also broken down the total amount into its components and illustrated the effect of compounding.

The formula for compound interest is a powerful tool that can be used to calculate the total amount paid over a period of time. By understanding how the formula works, we can make informed decisions about our finances and plan for the future.

References

Additional Resources

Introduction

In our previous article, we delved into the world of mathematics and explored the concept of compound interest. Suzanne, a car buyer, has purchased a vehicle with a list price of $23,860. She has traded in her previous car and financed the remaining cost for five years at a rate of 11.62%, compounded monthly. We used mathematical formulas to calculate the total amount Suzanne will pay over the five-year period.

In this article, we will answer some frequently asked questions related to Suzanne's car purchase and compound interest.

Q&A

Q: What is compound interest?

A: Compound interest is the interest earned on both the principal amount and any accrued interest over time. It is calculated using the formula:

A = P(1 + r/n)^(nt)

Where:

  • A is the amount of money accumulated after n years, including interest
  • P is the principal amount (the initial amount of money)
  • r is the annual interest rate (in decimal form)
  • n is the number of times that interest is compounded per year
  • t is the time the money is invested for, in years

Q: How does compounding work?

A: Compounding works by applying the interest rate to the principal amount at the end of each compounding period. In the case of Suzanne's car purchase, the interest is compounded monthly, so the interest rate is applied to the principal amount at the end of each month.

Q: What is the effect of compounding on the total amount paid?

A: The effect of compounding is to increase the total amount paid over time. In the case of Suzanne's car purchase, the total amount paid over the five-year period is approximately $38,419.19, which is higher than the principal amount of $23,860.

Q: How can I calculate the total amount paid using the compound interest formula?

A: To calculate the total amount paid using the compound interest formula, you need to plug in the values for the principal amount, interest rate, compounding frequency, and time period. You can use a calculator or a spreadsheet to make the calculation easier.

Q: What is the difference between simple interest and compound interest?

A: Simple interest is calculated as a percentage of the principal amount, while compound interest is calculated as a percentage of the principal amount and any accrued interest. Compound interest is typically higher than simple interest because it takes into account the interest earned on the interest.

Q: How can I avoid paying too much interest on a loan?

A: To avoid paying too much interest on a loan, you can consider the following options:

  • Paying off the loan as quickly as possible
  • Making extra payments towards the principal amount
  • Choosing a loan with a lower interest rate
  • Considering a loan with a longer repayment period

Q: What is the impact of inflation on compound interest?

A: Inflation can have a negative impact on compound interest because it reduces the purchasing power of the money. However, some loans and investments may offer inflation-indexed interest rates, which can help to keep pace with inflation.

Conclusion

In this article, we have answered some frequently asked questions related to Suzanne's car purchase and compound interest. We hope this information has been helpful in understanding the concept of compound interest and how it can affect the total amount paid over time.

References

Additional Resources