1. Understanding and Appreciating the Time Value of Money
Chapter 3
Understanding and Appreciating the Time Value of Money

2. Introduction
Always comparing money from different time periods – a dollar received today is worth more than a dollar received in the future. Why is that?
Everything in personal finance involves time value of money

3. Compound Interest and Future Values
Interest paid on interest.
Reinvestment of interest paid on an investment’s principal
Principal is the face value of the deposit or debt instrument.

4. How Compound Interest Works
Future value—the value of an investment at some point in the future
Present value—the current value in today’s dollars of a future sum of money
Facts of Life page 67

5. Figure 3.1 Compound Interest at 6 Percent Over Time

6. Ways to Calculate TVM Formulas Financial calculators*
Spreadsheets (ex: Excel)

7. The Rule of 72 How long will it take to double your money?
Numbers of years for a given sum to double by dividing the investment’s annual growth or interest rate into 72.

8. The Rule of 72
Example: If an investment grows at an annual rate of 9% per year, then it should take 72/9 = 8 years to double.

9. Calculator Clues Before solving problem: Working a problem:
Set to one payment per year
Set to display at least four decimal places
Set to “end” mode
Working a problem:
Positive and negative numbers – 1 negative number for each equation
Enter zero for variables not in the problem
Enter interest rate as a %, 10 not 0.10

10. Calculating the Future Value of a Single Sum
Example:
What will $5000 grow to become
if invested at 10% for 6 years?

11. Calculating the Future Value of a Single Sum
Chapter 2
Calculating the Future Value of a Single Sum
Calculator
N = 6
I/Y = 10
PV = -5000
PMT = 0
CPT FV

12. Compound Interest with Nonannual Periods
Compounding may be quarterly, monthly, daily, or even a continuous basis.
Money grows faster as the compounding period becomes shorter.
Interest earned on interest more frequently grows money faster.

13. Compound Interest with Nonannual Periods
Interest is often compounded monthly, quarterly, or semiannually in the real world
Adjustments must be made to calculations and formulas
the number of years, N, is multiplied by the number of compounding periods, m
Divided I/Y by m
Make m = number of compounding periods per year.

14. Calculating the Future Value of a Single Sum
Chapter 2
Calculating the Future Value of a Single Sum
Calculator
N = 2 x m
I/Y = 8/m
PV = -100
PMT = 0
CPT FV

15. Chapter 2
Calculating the Future Value of a Single Sum of $100 for 2 years compounded quarterly
Calculator
N = 2 x 4
I/Y = 8 / 4
PV = -100
PMT = 0
CPT FV

16. The Importance of the Interest Rate
The interest rate plays a critical role in how much an investment grows.
Time is important also.
Stop & Think page 72
Daily compounding – 1 cent compounded daily for 31 days at 100% interest.

17. Growth of $1,000 at 8 % interest
Years

18. Growth of $1000 at 10% interest
45,259
21,725
Years

19. Present Value What’s it worth in today’s dollars?
Strip away inflation to see what future cash flows are worth today.
Inverse of compounding.
Discount rate is the interest rate used to bring future money back to present.

20. Present Value Example
You’re on vacation in Florida and you see an advertisement stating that you’ll receive $100 simply for taking a tour of a model condominium.
You discover that the $100 is in the form of a savings bond that will not pay you the $100 for 10 years.
What is the PV of the $100 to be received 10 years from today if your discount rate is 6%?

21. Calculating the Present Value of a Single Sum
Chapter 2
Calculating the Present Value of a Single Sum
Calculator
N = 10
I/Y = 6
FV = 100
PMT = 0
CPT PV

22. Annuities
An annuity is a series of equal dollar payments coming at the end of each time period for a specific number of time period.
Depositing an equal amount of money at the end of a specific time period and allowing it to grow – investing in a college education

23. Calculating the Future Value of an Annuity
Example:
What would you accumulate if you could invest $5000 every year for the next 6 years at 10%? Assume the first investment occurs a year from today.

24. Calculating the Future Value of a Single Sum
Chapter 2
Calculating the Future Value of a Single Sum
Calculator
N = 6
I/Y = 10
PV = 0
PMT = 5000
CPT FV

25. Annuities Example
You’ll need $10,000 for education in 8 years. How much must you put away at the end of each year at 6% interest to have the college money ready?

26. Calculating the Future Value of an annuity
Chapter 2
Calculating the Future Value of an annuity
Calculator
N = 8
I/Y = 6
PV = 0
FV = 10000
CPT PMT

27. Compound Annuities Example
If you deposit $2,000 in an individual retirement account (IRA) at the end of each year and it grows at a rate of 10% per year, how much will you have when you retire in 30 years?

28. Calculating the Future Value of an annuity
Chapter 2
Calculating the Future Value of an annuity
Calculator
N = 30
I/Y = 10
PV = 0
PMT = 2000
CPT FV

29. Amortized Loans
Loans paid off in equal installments. (mortgage and car payments)
You borrow $16,000 at 8% interest to buy a car and repay it in 4 equal payments at the end of each of the next 4 years. What are the annual payments?

30. Calculating the Future Value of a Single Sum
Chapter 2
Calculating the Future Value of a Single Sum
Calculator
N = 4
I/Y = 8
PV =
FV = 0
CPT PMT
FIN 261 Personal Finance

31. Let’s work more problems

32. Problem 1
How much would you have if you invest $100 today, earning 6% annually, you hold the investment for 5 years?
What if the interest is compounded monthly?

33. Problem 2
Let’s say your aunt gave you a EE savings bond that will be worth $100 in 5 years earning 4.5% annually. What is its value today?

34. Problem 3
What is the future value of an ordinary annuity if $100 payments occur for 10 years, and you can earn a 7% return?

35. Problem 4
You just won the lottery and will receive $100,000 at the end of each of the next 20 years. Alternatively, you can take the value in a lump sum today. If the appropriate rate is 8%, what should the lump sum be?

36. Problem 5
An investment advisor recommends you buy an annuity that will pay $1,000 at the end of each year for the next 10 years. What should you pay for this annuity if you can earn a 9% return?

37. Problem6
What is the monthly payment for principal and interest on a $150,000 mortgage priced at 7.2% for 30 years?

38. Problem 7
An investor expects to earn a 9.1% return. How long will it take to double the investment?