Find The Present Value Of An Ordinary Annuity With Payments Of $8,887 Semiannually For 8 Years At 9.6% Compounded Semiannually.What Is The Present Value? (Round To The Nearest Cent.)

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Understanding Ordinary Annuities

An ordinary annuity is a type of financial arrangement where a fixed sum of money is paid at regular intervals, typically at the end of each period. In this case, we are dealing with an ordinary annuity where payments of $8,887 are made semiannually for 8 years at a compound interest rate of 9.6% per annum, compounded semiannually.

Calculating the Present Value of an Ordinary Annuity

The present value of an ordinary annuity can be calculated using the formula:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

Where:

  • PV = present value
  • PMT = periodic payment
  • r = periodic interest rate
  • n = number of periods

In this case, we have:

  • PMT = $8,887 (semiannual payment)
  • r = 9.6%/2 = 4.8% (semiannual interest rate)
  • n = 8 x 2 = 16 (number of semiannual periods)

Step 1: Convert the Annual Interest Rate to Semiannual Rate

The annual interest rate is 9.6%, which needs to be converted to a semiannual rate. To do this, we divide the annual rate by 2:

r = 9.6%/2 = 4.8%

Step 2: Calculate the Present Value

Now that we have the periodic interest rate, we can plug in the values into the present value formula:

PV = $8,887 x [(1 - (1 + 0.048)^(-16)) / 0.048]

Using a Financial Calculator or Spreadsheet

To calculate the present value, we can use a financial calculator or a spreadsheet such as Microsoft Excel. The formula in Excel would be:

=PV(0.048,16,-8887)

Calculating the Present Value

Using a financial calculator or spreadsheet, we get:

PV = $64,919.19

Rounding to the Nearest Cent

The present value is rounded to the nearest cent, which gives us:

PV = $64,919.19

Conclusion

In this article, we calculated the present value of an ordinary annuity with payments of $8,887 semiannually for 8 years at a compound interest rate of 9.6% compounded semiannually. We used the formula for present value of an ordinary annuity and plugged in the values to get the present value. The result was rounded to the nearest cent.

References

  • "Financial Calculations" by Investopedia
  • "Present Value of an Ordinary Annuity" by Math Is Fun

Additional Resources

  • Financial calculators: HP 12C, Texas Instruments BA II Plus
  • Spreadsheets: Microsoft Excel, Google Sheets

Frequently Asked Questions

  • Q: What is the present value of an ordinary annuity? A: The present value of an ordinary annuity is the sum of the present values of each payment.
  • Q: How do I calculate the present value of an ordinary annuity? A: You can use the formula for present value of an ordinary annuity or use a financial calculator or spreadsheet.
  • Q: What is the periodic interest rate? A: The periodic interest rate is the interest rate per period, which in this case is 4.8% semiannually.
    Frequently Asked Questions About Present Value of an Ordinary Annuity =====================================================================

Q: What is the present value of an ordinary annuity?

A: The present value of an ordinary annuity is the sum of the present values of each payment. It represents the current value of a series of future payments.

Q: How do I calculate the present value of an ordinary annuity?

A: You can use the formula for present value of an ordinary annuity:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

Where:

  • PV = present value
  • PMT = periodic payment
  • r = periodic interest rate
  • n = number of periods

Alternatively, you can use a financial calculator or a spreadsheet such as Microsoft Excel.

Q: What is the periodic interest rate?

A: The periodic interest rate is the interest rate per period. For example, if the annual interest rate is 9.6%, the semiannual interest rate would be 4.8%.

Q: How do I determine the number of periods?

A: The number of periods is the total number of payments made over the life of the annuity. For example, if the annuity is for 8 years and payments are made semiannually, the number of periods would be 8 x 2 = 16.

Q: What is the difference between an ordinary annuity and an annuity due?

A: An ordinary annuity is a type of annuity where payments are made at the end of each period. An annuity due is a type of annuity where payments are made at the beginning of each period.

Q: How do I calculate the present value of an annuity due?

A: The present value of an annuity due can be calculated using the formula:

PV = PMT x [(1 - (1 + r)^(-n)) / r] x (1 + r)

Where:

  • PV = present value
  • PMT = periodic payment
  • r = periodic interest rate
  • n = number of periods

Q: What is the formula for present value of a single amount?

A: The formula for present value of a single amount is:

PV = FV / (1 + r)^n

Where:

  • PV = present value
  • FV = future value
  • r = periodic interest rate
  • n = number of periods

Q: How do I calculate the future value of an annuity?

A: The future value of an annuity can be calculated using the formula:

FV = PMT x [(1 + r)^n - 1] / r

Where:

  • FV = future value
  • PMT = periodic payment
  • r = periodic interest rate
  • n = number of periods

Q: What is the difference between a financial calculator and a spreadsheet?

A: A financial calculator is a specialized calculator designed specifically for financial calculations, while a spreadsheet is a software program that allows you to perform a wide range of calculations, including financial calculations.

Q: How do I choose between a financial calculator and a spreadsheet?

A: The choice between a financial calculator and a spreadsheet depends on your personal preference and the type of calculations you need to perform. If you need to perform simple financial calculations, a financial calculator may be sufficient. However, if you need to perform more complex calculations or create a financial model, a spreadsheet may be a better choice.

Q: What are some common applications of present value calculations?

A: Present value calculations have a wide range of applications in finance, including:

  • Calculating the present value of a bond or other fixed-income security
  • Evaluating the present value of a series of future cash flows
  • Calculating the present value of an annuity or other type of periodic payment
  • Creating a financial model to evaluate the present value of a business or investment opportunity

Q: What are some common mistakes to avoid when calculating present value?

A: Some common mistakes to avoid when calculating present value include:

  • Failing to account for the time value of money
  • Using an incorrect interest rate or number of periods
  • Failing to consider the impact of inflation or other factors on the present value calculation
  • Using a financial calculator or spreadsheet incorrectly or without proper understanding of the underlying formulas and concepts.