Math 1324: Lab 3 - Chapter 5You Must Show All Your Work In The Space Provided To Receive Full Credit For Each Problem. Final Answers Must Be Simplified And Circled. If You Use A TVM Solver, Make Sure To Show The Algebraic Formula With The Values You

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Introduction

In this lab, we will be exploring the concepts of time value of money (TVM) and its applications in finance. We will be using the formulas and techniques learned in Chapter 5 to solve various problems related to TVM. It is essential to show all work and simplify final answers to receive full credit for each problem.

Problem 1: Present Value of a Single Sum

Problem Statement

A company wants to invest $10,000 in a project that will generate a return of 8% per annum for 5 years. What is the present value of this investment?

Solution

To find the present value of a single sum, we use the formula:

PV = FV / (1 + r)^n

where:

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

Given values:

  • FV = $10,000
  • r = 8% = 0.08
  • n = 5 years

Substituting the values in the formula, we get:

PV = $10,000 / (1 + 0.08)^5 PV = $10,000 / (1.08)^5 PV = $10,000 / 1.469004 PV = $6,813.19

Answer: $6,813.19

Problem 2: Future Value of a Single Sum

Problem Statement

A person invests $5,000 in a savings account that earns an interest rate of 6% per annum. What will be the future value of this investment after 10 years?

Solution

To find the future value of a single sum, we use the formula:

FV = PV x (1 + r)^n

where:

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

Given values:

  • PV = $5,000
  • r = 6% = 0.06
  • n = 10 years

Substituting the values in the formula, we get:

FV = $5,000 x (1 + 0.06)^10 FV = $5,000 x (1.06)^10 FV = $5,000 x 1.790848 FV = $8,954.24

Answer: $8,954.24

Problem 3: Present Value of an Annuity

Problem Statement

A company wants to invest $2,000 per year for 5 years in a project that will generate a return of 8% per annum. What is the present value of this investment?

Solution

To find the present value of an annuity, we use the formula:

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

where:

  • PV = present value
  • PMT = annual payment
  • r = interest rate
  • n = number of years

Given values:

  • PMT = $2,000
  • r = 8% = 0.08
  • n = 5 years

Substituting the values in the formula, we get:

PV = $2,000 x [(1 - (1 + 0.08)^(-5)) / 0.08] PV = $2,000 x [(1 - (1.08)^(-5)) / 0.08] PV = $2,000 x [(1 - 0.677419) / 0.08] PV = $2,000 x (0.322581 / 0.08) PV = $2,000 x 4.028 PV = $8,056

Answer: $8,056

Problem 4: Future Value of an Annuity

Problem Statement

A person invests $1,500 per year for 10 years in a savings account that earns an interest rate of 6% per annum. What will be the future value of this investment?

Solution

To find the future value of an annuity, we use the formula:

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

where:

  • FV = future value
  • PMT = annual payment
  • r = interest rate
  • n = number of years

Given values:

  • PMT = $1,500
  • r = 6% = 0.06
  • n = 10 years

Substituting the values in the formula, we get:

FV = $1,500 x [(1 + 0.06)^10 - 1] / 0.06 FV = $1,500 x [(1.06)^10 - 1] / 0.06 FV = $1,500 x (1.790848 - 1) / 0.06 FV = $1,500 x 0.790848 / 0.06 FV = $1,500 x 13.18147 FV = $17,474.21

Answer: $17,474.21

Conclusion

In this lab, we have explored the concepts of time value of money (TVM) and its applications in finance. We have used the formulas and techniques learned in Chapter 5 to solve various problems related to TVM. The present value and future value of single sums and annuities have been calculated using the respective formulas. These calculations have provided us with a deeper understanding of the time value of money and its importance in financial decision-making.

References

  • [1] Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of corporate finance. McGraw-Hill Education.
  • [2] Ross, S. A., Westerfield, R. W., & Jaffe, J. F. (2017). Corporate finance. McGraw-Hill Education.
  • [3] Bodie, Z., Kane, A., & Marcus, A. J. (2017). Investments. McGraw-Hill Education.

Note

Introduction

In this Q&A section, we will address some common questions related to the concepts of time value of money (TVM) and its applications in finance. We will provide detailed explanations and examples to help clarify any doubts.

Q1: What is the time value of money?

A1: The time value of money (TVM) refers to the concept that money received today is worth more than the same amount of money received in the future. This is because money received today can be invested to earn interest, making it more valuable than the same amount of money received in the future.

Q2: What is the difference between present value and future value?

A2: Present value (PV) is the value of a future amount of money today, while future value (FV) is the value of a present amount of money in the future. For example, if you receive $1,000 today, its present value is $1,000. However, if you receive $1,000 in 5 years, its future value is $1,000 x (1 + r)^5, where r is the interest rate.

Q3: How do you calculate the present value of a single sum?

A3: To calculate the present value of a single sum, you use the formula:

PV = FV / (1 + r)^n

where:

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

Q4: How do you calculate the future value of a single sum?

A4: To calculate the future value of a single sum, you use the formula:

FV = PV x (1 + r)^n

where:

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

Q5: What is the difference between the present value of an annuity and the future value of an annuity?

A5: The present value of an annuity is the value of a series of future payments today, while the future value of an annuity is the value of a series of present payments in the future. For example, if you receive $1,000 per year for 5 years, its present value is the sum of the present values of each payment, while its future value is the sum of the future values of each payment.

Q6: How do you calculate the present value of an annuity?

A6: To calculate the present value of an annuity, you use the formula:

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

where:

  • PV = present value
  • PMT = annual payment
  • r = interest rate
  • n = number of years

Q7: How do you calculate the future value of an annuity?

A7: To calculate the future value of an annuity, you use the formula:

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

where:

  • FV = future value
  • PMT = annual payment
  • r = interest rate
  • n = number of years

Q8: What is the importance of time value of money in finance?

A8: The time value of money is essential in finance because it helps investors and businesses make informed decisions about investments and financial transactions. It takes into account the fact that money received today is worth more than the same amount of money received in the future, and it helps to calculate the present and future values of investments and financial transactions.

Conclusion

In this Q&A section, we have addressed some common questions related to the concepts of time value of money (TVM) and its applications in finance. We have provided detailed explanations and examples to help clarify any doubts. The time value of money is a fundamental concept in finance, and it is essential to understand its importance and applications in order to make informed decisions about investments and financial transactions.

References

  • [1] Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of corporate finance. McGraw-Hill Education.
  • [2] Ross, S. A., Westerfield, R. W., & Jaffe, J. F. (2017). Corporate finance. McGraw-Hill Education.
  • [3] Bodie, Z., Kane, A., & Marcus, A. J. (2017). Investments. McGraw-Hill Education.