Caden Has An Offer To Buy An Item With A Sticker Price Of $\$7400$ By Paying $\$190$ A Month For 48 Months. Which Of These Groups Of Values Plugged Into The TVM Solver Of A Graphing Calculator Will Give Him The Correct Answer For The

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Caden is presented with an offer to purchase an item with a sticker price of $7400\$7400 by paying $190\$190 a month for 48 months. To determine the correct answer for the present value of this annuity, we need to use a TVM (Time Value of Money) Solver on a graphing calculator. In this article, we will explore the different groups of values that can be plugged into the TVM Solver to obtain the correct answer.

The TVM Solver: A Powerful Tool for Time Value of Money Calculations

The TVM Solver is a powerful tool that allows us to calculate various time value of money metrics, including the present value of an annuity. To use the TVM Solver, we need to input the following values:

  • PV (Present Value): The future value of the annuity, which is the sticker price of the item, $7400\$7400.
  • FV (Future Value): The future value of the annuity, which is the sticker price of the item, $7400\$7400.
  • PMT (Payment): The monthly payment, $190\$190.
  • N (Number of Payments): The number of payments, 48 months.
  • I/Y (Interest Rate per Period): The interest rate per period, which is not given in the problem.
  • CPT (Calculate): The TVM Solver will calculate the present value of the annuity.

Calculating the Present Value of the Annuity

To calculate the present value of the annuity, we need to input the following values into the TVM Solver:

  • PV: $7400\$7400
  • FV: $7400\$7400
  • PMT: $190\$190
  • N: 48
  • I/Y: ? (we will assume an interest rate of 0% for now)

By inputting these values into the TVM Solver, we can calculate the present value of the annuity.

The Correct Answer: Present Value of the Annuity

After inputting the values into the TVM Solver, we get the following result:

  • PV: $7400\$7400
  • FV: $7400\$7400
  • PMT: $190\$190
  • N: 48
  • I/Y: 0%
  • CPT: Present Value of the Annuity = $7400\$7400

However, this is not the correct answer. The correct answer is the present value of the annuity, which is the sticker price of the item minus the present value of the payments.

The Present Value of the Payments

To calculate the present value of the payments, we need to use the formula for the present value of an annuity:

  • PV: $190\$190 x (1 - (1 + 0.05)^(-48))
  • FV: $0\$0
  • PMT: $190\$190
  • N: 48
  • I/Y: 0.05

By inputting these values into the TVM Solver, we get the following result:

  • PV: $190\$190 x (1 - (1 + 0.05)^(-48)) = $6,419.19\$6,419.19

The Correct Answer: Present Value of the Annuity

Now that we have calculated the present value of the payments, we can calculate the present value of the annuity:

  • PV: $7400\$7400 - $6,419.19\$6,419.19 = $980.81\$980.81

Therefore, the correct answer is $980.81\$980.81.

Conclusion

In this article, we explored the different groups of values that can be plugged into the TVM Solver to obtain the correct answer for the present value of an annuity. We calculated the present value of the payments using the formula for the present value of an annuity and then subtracted this value from the sticker price of the item to obtain the correct answer. The correct answer is $980.81\$980.81.

References

  • TVM Solver: A Powerful Tool for Time Value of Money Calculations
  • Present Value of an Annuity Formula
  • Time Value of Money Calculations

Keywords

  • TVM Solver
  • Present Value of an Annuity
  • Time Value of Money Calculations
  • Annuity
  • Present Value
  • Future Value
  • Payment
  • Number of Payments
  • Interest Rate per Period
  • Calculate
    Frequently Asked Questions: TVM Solver and Present Value of an Annuity ====================================================================

In this article, we will answer some of the most frequently asked questions about the TVM Solver and the present value of an annuity.

Q: What is the TVM Solver?

A: The TVM Solver is a powerful tool that allows us to calculate various time value of money metrics, including the present value of an annuity. It is a feature on graphing calculators that can be used to solve problems involving time value of money.

Q: What is the present value of an annuity?

A: The present value of an annuity is the value of a series of payments made at regular intervals over a period of time. It is calculated by discounting the future payments to their present value.

Q: How do I use the TVM Solver to calculate the present value of an annuity?

A: To use the TVM Solver to calculate the present value of an annuity, you need to input the following values:

  • PV (Present Value): The future value of the annuity, which is the sticker price of the item.
  • FV (Future Value): The future value of the annuity, which is the sticker price of the item.
  • PMT (Payment): The monthly payment.
  • N (Number of Payments): The number of payments.
  • I/Y (Interest Rate per Period): The interest rate per period.
  • CPT (Calculate): The TVM Solver will calculate the present value of the annuity.

Q: What is the formula for the present value of an annuity?

A: The formula for the present value of an annuity is:

  • PV: $PMT\$PMT x (1 - (1 + rn\frac{r}{n})^(-n×tn \times t))

Where:

  • PV: Present value of the annuity
  • PMT: Monthly payment
  • r: Annual interest rate
  • n: Number of times interest is compounded per year
  • t: Number of years

Q: How do I calculate the present value of the payments?

A: To calculate the present value of the payments, you need to use the formula for the present value of an annuity:

  • PV: $PMT\$PMT x (1 - (1 + rn\frac{r}{n})^(-n×tn \times t))

Where:

  • PV: Present value of the payments
  • PMT: Monthly payment
  • r: Annual interest rate
  • n: Number of times interest is compounded per year
  • t: Number of years

Q: What is the difference between the present value of the annuity and the present value of the payments?

A: The present value of the annuity is the value of the entire annuity, including the present value of the payments and the present value of the future value of the annuity. The present value of the payments is the value of the payments made at regular intervals over a period of time.

Q: How do I calculate the interest rate per period?

A: To calculate the interest rate per period, you need to divide the annual interest rate by the number of times interest is compounded per year.

Q: What is the interest rate per period?

A: The interest rate per period is the interest rate divided by the number of times interest is compounded per year.

Q: How do I calculate the number of times interest is compounded per year?

A: To calculate the number of times interest is compounded per year, you need to divide 1 by the interest rate per period.

Q: What is the number of times interest is compounded per year?

A: The number of times interest is compounded per year is 1 divided by the interest rate per period.

Conclusion

In this article, we answered some of the most frequently asked questions about the TVM Solver and the present value of an annuity. We provided formulas and examples to help you understand how to use the TVM Solver to calculate the present value of an annuity.

References

  • TVM Solver: A Powerful Tool for Time Value of Money Calculations
  • Present Value of an Annuity Formula
  • Time Value of Money Calculations

Keywords

  • TVM Solver
  • Present Value of an Annuity
  • Time Value of Money Calculations
  • Annuity
  • Present Value
  • Future Value
  • Payment
  • Number of Payments
  • Interest Rate per Period
  • Calculate