Find The Present Value Of An Ordinary Annuity Which Has Payments Of $ 2100 \$2100 $2100 Per Year For 15 Years At 6 % 6\% 6% Compounded Annually.What Formula Is Used To Find The Present Value? Select The Correct Answer Below And Fill In The Answer

What is an Ordinary Annuity?

An ordinary annuity is a type of annuity where a fixed amount of money is paid at regular intervals, typically at the end of each period. In this case, we have an ordinary annuity with annual payments of $\$2100$ for 15 years.

The Formula for 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 is the present value of the annuity
• PMT is the annual payment amount
• r is the annual interest rate (in decimal form)
• n is the number of years

How to Use the Formula

To find the present value of the ordinary annuity, we need to plug in the values into the formula:

• PMT = $\$2100$
• r = $6\%$ = $0.06$
• n = 15 years

Calculating the Present Value

Now, let's calculate the present value using the formula:

PV = $\$2100$ x [(1 - (1 + 0.06)^(-15)) / 0.06]

PV = $\$2100$ x [(1 - (1.06)^(-15)) / 0.06]

PV = $\$2100$ x [(1 - 0.418) / 0.06]

PV = $\$2100$ x (0.582 / 0.06)

PV = $\$2100$ x 9.7

PV = $\$20,337$

Conclusion

The present value of the ordinary annuity with annual payments of $\$2100$ for 15 years at $6\%$ compounded annually is $\$20,337$. This formula can be used to calculate the present value of any ordinary annuity by plugging in the values of the annual payment amount, interest rate, and number of years.

Example Use Cases

This formula can be used in various financial scenarios, such as:

• Calculating the present value of a mortgage or a car loan
• Determining the present value of a series of investments
• Evaluating the present value of a business or a project

Limitations of the Formula

While this formula is useful for calculating the present value of an ordinary annuity, it assumes that the interest rate remains constant over the entire period. In reality, interest rates may fluctuate, and this formula may not accurately reflect the actual present value of the annuity.

Alternatives to the Formula

There are alternative methods to calculate the present value of an ordinary annuity, such as using a financial calculator or a spreadsheet. However, the formula provided above is a simple and effective way to calculate the present value of an ordinary annuity.

Conclusion

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

A: An ordinary annuity is a type of annuity where a fixed amount of money is paid at the end of each period, whereas an annuity due is a type of annuity where a fixed amount of money is paid at the beginning of each period.

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

A: To calculate the present value of an annuity due, you can use the formula:

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

Where:

• PV is the present value of the annuity
• PMT is the annual payment amount
• r is the annual interest rate (in decimal form)
• n is the number of years

Q: What is the formula for calculating the future value of an ordinary annuity?

A: The formula for calculating the future value of an ordinary annuity is:

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

Where:

• FV is the future value of the annuity
• PMT is the annual payment amount
• r is the annual interest rate (in decimal form)
• n is the number of years

Q: How do I calculate the present value of a series of investments?

A: To calculate the present value of a series of investments, you can use the formula:

PV = Σ (PMT x (1 + r)^(-n))

Where:

• PV is the present value of the series of investments
• PMT is the annual payment amount
• r is the annual interest rate (in decimal form)
• n is the number of years
• Σ represents the sum of the series

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

A: The present value of an annuity is the value of the annuity today, whereas the future value of an annuity is the value of the annuity at a future date.

Q: How do I calculate the present value of a business or a project?

A: To calculate the present value of a business or a project, you can use the formula:

PV = Σ (PMT x (1 + r)^(-n))

Where:

• PV is the present value of the business or project
• PMT is the annual payment amount
• r is the annual interest rate (in decimal form)
• n is the number of years
• Σ represents the sum of the series

Q: What are some common applications of the present value formula?

A: The present value formula has many applications in finance, including:

• Calculating the present value of a mortgage or a car loan
• Determining the present value of a series of investments
• Evaluating the present value of a business or a project
• Calculating the present value of an annuity due

Q: What are some common mistakes to avoid when using the present value formula?

A: Some common mistakes to avoid when using the present value formula include:

• Forgetting to convert the interest rate to decimal form
• Forgetting to use the correct formula for the type of annuity
• Forgetting to calculate the present value for each period
• Forgetting to sum the present values for each period

Q: How do I choose the correct formula for my specific situation?

A: To choose the correct formula for your specific situation, you need to determine the type of annuity, the interest rate, and the number of years. You can then use the formula that corresponds to your specific situation.

Conclusion

In conclusion, the present value formula is a powerful tool for calculating the value of an annuity today. By understanding the different types of annuities and the formulas for calculating their present value, you can make informed decisions about your financial investments. Remember to choose the correct formula for your specific situation and to avoid common mistakes when using the present value formula.