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# Understanding the Time Value of Money; Single Payment

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Introductory lecture on the time value of money for non-finance majors.

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### Understanding the Time Value of Money; Single Payment

1. 1.  Calculators must be set to 4 decimal places Calculators must be set to 1 payment per year
2. 2. Chapter 3Understanding The Time Value of Money:
3. 3. Time Value of Money  A dollar received today is worth more than a dollar received in the future.  The sooner your money can earn interest, the faster the interest can earn interest.
4. 4. Interest and Compound Interest Interest (i) -- is the return you receive for investing your money. Compound interest -- is the interest that your investment earns on the interest that your investment previously earned. Inflation (r) – is when rising prices reduce the purchase power of money.
5. 5. The effect of 3% interest on aone time deposit of \$100 Reminders……3% = .03 in decimal form On your calculator hit the 3 key and then hit the % key (4th row from the top left hand side)
6. 6. The effect of 3% interest on aone time deposit of \$100 Deposit (\$X) + Deposit (\$X) times interest rate (i) = new account balance For example: \$100 (\$X) + \$ 3 [100 (.03) = \$X(.03)] \$103
7. 7. Or in one easy step: Your deposit (\$X) multiplied by (1 + the interest rate—in decimal form) = new acct. balance = \$X(1 + i) = new account balance = \$100(1.03) = \$103  \$X + \$X(i) = \$X(1 + i)
8. 8. The effect of compounding interestover time (long form) = \$X1 + [\$X1(i)] = \$X2 = \$X2 + [\$X2(i)] = \$X3 = \$X3 + [\$X3(i)] = \$X4 ………. = \$100x1 + [\$100x1(.03)] = \$103x2 = \$103x2 + [\$103x2(.03)] = \$106.09x3 = \$106.09x3 + [\$106.09x3(.03)] = \$109.27x4
9. 9. In other words (short form) X(1 + i)3 = X4 OR X(1 + i)n X = \$\$ deposit I = % interest rate Where n = number of periods you are compounding
10. 10. Practice problems How much will you have in savings if you deposit \$10 and leave it in an account earning 5% interest compounded annually for 10 years? How much will you have in savings if you deposit \$100 in an account earning 12% compounded annually for 20 years?
11. 11. No financial calculator 10 * 1.05 to the 10th  10(1.05)10
12. 12.  With your financial calculator you enter the number and then tell it where to go….. Key in -10 then hit the PV key Key in 5 then hit the i/y key (don’t change to decimal it does it for you) Key in 10 hit the N key Hit CPT FV key to show answer
13. 13. Financial Calculator…. PV = -10 (DOLLARS) I/Y = 5 (PERCENT) N = 10 (YEARS/PERIODS)  COMPUTE FV (FUTURE VALUE)
14. 14.  \$-16.28 ***your answer will show up as a negative number. That is expected because the \$10 was an outflow of cash from one’s current consumption to one’s retirement account. If you don’t want your answer to show up as negative then you have to remember to make the PV negative.
15. 15. Practice problems How much will you have in savings if you deposit \$100 in an account earning 12% compounded annually for 20 years?
16. 16. No financial calculator 100 * 1.12 to the 20th  100(1.12)20
17. 17.  With your financial calculator you enter the number and then tell it where to go….. Key in -100 then hit the PV key Key in 12 then hit the i/y key (don’t change to decimal it does it for you) Key in 20 hit the N key Hit CPT FV key to show answer
18. 18. Financial Calculator…. PV = -100 (DOLLARS) I/Y = 12 (PERCENT) N = 20 (YEARS/PERIODS)  COMPUTE FV (FUTURE VALUE)
19. 19.  \$-964.63 ***your answer will show up as a negative number. That is expected because the \$10 was an outflow of cash from one’s current consumption to one’s retirement account. If you don’t want your answer to show up as negative then you have to remember to make the PV negative.
20. 20. The Rule of 72 Estimates how many years an investment will take to double in value Number of years to double = 72 / annual compound growth rate (%) Example -- 72 / 8 = 9 therefore, it will take 9 years for an investment to double in value if it earns 8% annually
21. 21. Determining the Future Value ofyour Money over time Future value (FV) is the value to which your money will grow at a specific compounding interest rate (i). Future value is hypothetically moving your money forward (n) numbers of periods (days, months, years).
22. 22. Future Value Equation FV = PV(1 + i)n  FV = the future value of the investment at the end of (n) numbers of periods  i = the annual percentage (interest) rate (APR)  PV = the present value, in today’s dollars, of a sum of money This equation is used to determine the value of an investment at some point in the future.
23. 23. Future Value EquationFV = PV(1 + i)n
24. 24. Practice Problems: What is the future value (FV) of \$1,000 at the end of 15 years if it is invested in an account bearing 11% annually (APR)?
25. 25. Financial Calculators PV = -1000, N=15, I/Y = 11; CPT FV = \$4,784.58
26. 26. Practice Problems: What is the future value (FV) of \$1,500 after 20 years if it is invested in an account earning 8% annually (APR)?
27. 27. Financial Calculators PV = -1500, N = 20, I/Y = 8; CPT FV = \$6,991.44
28. 28. Bringing your money back from thefuture.
29. 29. Determining the Present Valueof your money Present Value (PV) Is hypothetically moving dollars from the future back into the present at a specific interest rate (i) for a specific number of periods (n) ―inverse compounding‖
30. 30. Present Value Equation PV = FV(1/(1 + i)n)  PV = the present value, in today’s dollars, of a sum of money  FV = the future value of the investment at the end of n years  i = annual interest rate (%)  n = number of periods This equation is used to determine today’s value of some future sum of money.
31. 31. Present Value EquationPV = FV[1/(1 + i)n]
32. 32. Practice Problems Josh is due to receive his inheritance (\$100,000) in 5 years. It is in an account earning 10% annually. Josh wants his money now. If Josh withdraws his money today, how much will he receive
33. 33. SolutionPV = FV[1/(1 + i)n]PV = -100,000[1/(1.10) 5]PV = \$62,092
34. 34. FINANCIAL CALCULATORS FV = -100,000N=5 I/Y = 10 CPT PV = 62,092
35. 35. Interest’s enemy: Inflation An economic condition in which rising prices reduce the purchasing power of money.
36. 36. Inflation adjusted interest rate (i*)Substitute i* for i during PV and FV formulas
37. 37.  I = the interest rate R = inflation rate
38. 38. Inflation adjusted interest rate (i*)FV = PV(1 + i*)n Controlling for inflationPV = FV[1/(1 + i*)n] Controlling for inflation
39. 39.  In your financial calculator the ―I‖ in I/Y is now replaced with I* (the inflation adjusted interest rate) You MUST calculate the I* first!!!!
40. 40. Summary FV = PV (1 + i)n  What your money will grow to be PV = FV (1/(1 + i)n  What your future money is worth today Inflation adjusted interest rate: (i*)  Substituting i* for i when controlling for inflation
41. 41. Next class… Chapter 3 part 2