If Quarterly Payments Are Made For 15 Years, Find The Value For { N $}$ In The Following Present Value Ordinary Annuity Formula:${ PV = P \left( \frac{1 - (1 + T)^{-n}}{t} \right) }$A. 45 B. 60 C. 15 D.

Understanding the Present Value of an Ordinary Annuity Formula

The present value of an ordinary annuity formula is a fundamental concept in finance and mathematics, used to calculate the current value of a series of future cash flows. In this article, we will delve into the formula and explore how to find the value of { n $}$ when quarterly payments are made for 15 years.

The Present Value of an Ordinary Annuity Formula

The present value of an ordinary annuity formula is given by:

${ PV = P \left( \frac{1 - (1 + t)^{-n}}{t} \right) }$

Where:

• $PV$ is the present value of the annuity
• $P$ is the periodic payment
• $t$ is the interest rate per period
• $n$ is the number of periods

Understanding the Variables

To find the value of { n $}$, we need to understand the variables involved in the formula. The periodic payment $P$ is the amount paid at the end of each period, while the interest rate per period $t$ is the rate at which the payment grows. The number of periods $n$ is the total number of payments made.

Quarterly Payments for 15 Years

In this problem, we are given that quarterly payments are made for 15 years. This means that the periodic payment $P$ is made at the end of each quarter, and the interest rate per period $t$ is the quarterly interest rate. The number of periods $n$ is 15 years multiplied by 4 quarters per year, which equals 60 periods.

Finding the Value of { n $}$

To find the value of { n $}$, we can plug in the values of the variables into the formula. However, we are not given the values of $P$ and $t$. Instead, we are given the options A, B, C, and D, which correspond to the values 45, 60, 15, and an unknown value, respectively.

Analyzing the Options

Let's analyze the options and see which one is the most likely value of { n $}$. Option A is 45, which is less than the total number of periods. Option B is 60, which is equal to the total number of periods. Option C is 15, which is less than the total number of periods.

Conclusion

Based on the analysis, the most likely value of { n $}$ is 60. This is because the total number of periods is 60, and option B corresponds to this value.

The Final Answer

The final answer is B.
Q&A: Understanding the Present Value of an Ordinary Annuity Formula

In our previous article, we explored the present value of an ordinary annuity formula and how to find the value of { n $}$ when quarterly payments are made for 15 years. In this article, we will answer some frequently asked questions about the formula and provide additional insights.

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

A: The present value of an ordinary annuity formula is a mathematical formula used to calculate the current value of a series of future cash flows. It is given by:

${ PV = P \left( \frac{1 - (1 + t)^{-n}}{t} \right) }$

Where:

• $PV$ is the present value of the annuity
• $P$ is the periodic payment
• $t$ is the interest rate per period
• $n$ is the number of periods

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

A: An ordinary annuity is a series of payments made at the end of each period, while an annuity due is a series of payments made at the beginning of each period. The present value of an annuity due formula is given by:

${ PV = P \left( \frac{(1 + t)^n - 1}{t} \right) }$

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

A: To calculate the present value of an annuity in Excel, you can use the PV function. The syntax for the PV function is:

${ PV = PV(rate,nper,pmt,fv,type) }$

Where:

• $rate$ is the interest rate per period
• $nper$ is the number of periods
• $pmt$ is the periodic payment
• $fv$ is the future value of the annuity (optional)
• $type$ is the type of annuity (0 for ordinary annuity, 1 for annuity due)

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

A: The formula for the future value of an annuity is given by:

${ FV = P \left( \frac{(1 + t)^n - 1}{t} \right) }$

Where:

• $FV$ is the future value of the annuity
• $P$ is the periodic payment
• $t$ is the interest rate per period
• $n$ is the number of periods

Q: How do I calculate the present value of a growing annuity?

A: To calculate the present value of a growing annuity, you can use the following formula:

${ PV = \sum_{i=1}^{n} \frac{P_i}{(1 + t)^i} }$

Where:

• $PV$ is the present value of the annuity
• $P_i$ is the periodic payment at period $i$
• $t$ is the interest rate per period
• $n$ is the number of periods

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

A: The formula for the present value of a perpetual annuity is given by:

${ PV = \frac{P}{t} }$

Where:

• $PV$ is the present value of the annuity
• $P$ is the periodic payment
• $t$ is the interest rate per period

Conclusion

In this article, we answered some frequently asked questions about the present value of an ordinary annuity formula and provided additional insights. We hope that this article has been helpful in understanding the formula and its applications.