1. Compound Interest and Present Value
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2. PERFORMANCE OBJECTIVES
Section I Compound Interest—The Time Value of Money 11-1: Manually calculating compound amount (future value) and compound interests 11-2: Computing compound amount (future value) and compound interest by using compound interest tables 11-3: Creating compound interest table factors for periods beyond the table 11-4: Calculating annual percentage yield (APY) or effective interest rate 11-5: Calculating compound amount (future value) by using the compound interest formula
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a publicly accessible website, in whole or in part.

3. PERFORMANCE OBJECTIVES
continued
Section II Present Value 11-6: Calculating the present value of a future amount by using present value tables 11-7: Creating present value table factors for periods beyond the table 11-8: Calculating present value of a future amount by using the present value formula
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4. Compound Interest—The Time Value of Money
Interest that is applied a number of times during the term of a loan or investment.
Interest paid on principal and previously earned interest.
time value of money
The idea that money “now,” or in the present, is more desirable than the same amount of money in the future, because it can be invested and earn interest as time goes by.
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5. Compound Interest—The Time Value of Money
continued
compound amount, or future value (FV)
The total amount of principal and accumulated interest at the end of a loan or investment.
present amount, or present value (PV)
An amount of money that must be deposited today, at compound interest, to provide a specified lump sum of money in the future.
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a publicly accessible website, in whole or in part.

6. EXHIBIT 11-1 The Time Value of Money
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7. EXHIBIT 11-2 The Time Value of Money
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8. Manually Calculating Compound Interest
Using the simple interest formula, I = PRT, calculate the interest earned per period.
Each time interest is calculated, it is then added to the principal to determine the new principal.
Compound interest = Compound amount – Principal
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a publicly accessible website, in whole or in part.

9. Calculating Compound Interest Example
What is the compound amount and the compound interest of $10,000 at 12% interest, compounded semiannually for 3 years?
Original principal = 10,000.00
Interest period 1 = PRT = 10, × .12 × .5 =
Principal period 2 = 10,600.00
Interest period 2 = PRT = 10, × .12 × .5 =
Principal period 3 = 11,236.00
Interest period 3 = PRT = 11, × .12 × .5 =
Principal period 4 = 11,910.16
Interest period 4 = PRT = 11, × .12 × .5 =
Principal period 5 = 12,624.77
Interest period 5 = PRT = 12, × .12 × .5 =
Principal period 6 = 13,382.26
Interest period 6 = PRT = 13, × .12 × .5 =
Compound amount = 14,185.20
Original principal = -10,000.00
Compound interest = 4,185.20
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a publicly accessible website, in whole or in part.

10. Compound amount (future value) Compounding periods
Computing Compound Amount (Future Value) and Compound Interest By Using Compound Interest Tables
Compound amount (future value)
Table factor × Principal
Compounding periods
Years × Periods per year
Interest rate per period
Nominal rate Periods per year
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11. TABLE 11-1
Compound Interest Table (Future Value of $1 at Compound Interest)
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12. Compounding Periods per Year
EXHIBIT 11-3
Compounding Periods per Year
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13. For using compound interest tables
Step 1 Scan across the top row to find the interest rate per period.
Step 2 Look down that column to the row corresponding to the number of periods.
Step 3 The table factor at the intersection of the rate-per- period column and the number-of-periods row is the future value of $1 at compound interest. Multiply the table factor by the principal to determine the compound amount.
Compound amount = Table factor × Principal
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a publicly accessible website, in whole or in part.

14. Using Compound Interest Tables Example
Compounding periods = years  periods per year
Compounding periods =
Interest rate per period = nominal rate ÷ periods per year
Interest rate period =
Compound amount (FV) = table factor  principal
Compound amount (FV) =
Compound interest =
3 × 2 = 6
12% ÷ 2 = 6%
 10,000 =
14,185.20
14, – 10,000 =
4,185.20
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a publicly accessible website, in whole or in part.

15. For creating new compound interest table factors
Step 1 For the stated interest rate per period, find the two table factors that represent half, or values as close as possible to half, of the periods required.
Step 2 Multiply the two table factors from Step 1 to form the new factor.
Step 3 Round the new factor to five decimal places.
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a publicly accessible website, in whole or in part.

16. Creating Compound Interest Table Factors for Periods Beyond the Table Example
Calculate a new table factor and find the compound amount of $3,500 invested at 16% interest compounded quarterly, for 7 years.
Interest rate per period = 16% ÷ 4 = 4% 28
Compounding periods = 7  4 =
4%, 14 periods =
4%, 14 periods = 
28 periods
Rounded new table value =  3,500
Compounded amount = $10,495.52
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a publicly accessible website, in whole or in part.

17. Annual Percentage Yield (APY) or Effective Interest Rate
annual or nominal rate
The advertised or stated interest rate of an investment or loan.
The rate used to calculate the compound interest.
annual percentage yield (APY) or effective rate
The real or true rate of return on an investment.
It is the total compound interest earned in 1 year divided by the principal.
The more compounding periods per year, the higher the APY.
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a publicly accessible website, in whole or in part.

18. Compound Interest Earned on $100 at 12%
EXHIBIT 11-4
Compound Interest Earned on $100 at 12%
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19. Calculating Annual Percentage Yield (APY) or Effective Interest Rate
What is the compound amount, compound interest, and annual percentage yield of $7,000 invested for 1 year, at 6% interest, compounded quarterly.
Interest rate per period =
Compound periods =
Compound amount =
Compound interest =
6% ÷ 4 =
1.5%
1  4 = 4
 7,000 =
$7,429.52
7, – 7,000 =
$429.52
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a publicly accessible website, in whole or in part.

20. Calculating Compound Amount (Future Value) by Using the Compound Interest Formula
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a publicly accessible website, in whole or in part.

21. For using present value tables
Step 1 Add the 1 and the interest rate per period, i.
Step 2 Raise the sum from Step 1 to the nth (number of compounding periods) power by using the yx key on your calculator.
Step 3 Multiply the principal, P, by the answer from Step 2.
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a publicly accessible website, in whole or in part.

22. For using present value tables
Step 1 Scan across the top row to find the interest rate per period.
Step 2 Look down that column to the row corresponding to the number of periods.
Step 3 The table factor found at the intersection of the rate-per-period column and the number-of-periods row is the present value of $1 at compound interest. Multiply the table factor by the compound amount to determine the present value.
Present value = Table factor × Compound amount (future value)
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a publicly accessible website, in whole or in part.

23. Present Value to Future Value
EXHIBIT 11-5
Present Value to Future Value
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a publicly accessible website, in whole or in part.

24. TABLE 11-2
Present Value Table (Present Value of $1 at Compound Interest)
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a publicly accessible website, in whole or in part.

25. Calculating Present Value
Use Table 11-2 to find how much must be invested now at 8% interest compounded quarterly to have $3,000,000, 3 years from now.
Interest rate per period =
Compounding periods =
Present value =
8% ÷ 4 = 2%
3  4 = 12
 3,000,000 =
$2,365,470
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a publicly accessible website, in whole or in part.

26. For Creating New Table Factors
Step 1 For the stated interest rate per period, find the two table factors that represent half, or values as close as possible to half, of the periods required.
Step 2 Multiply the two table factors from Step 1 to form the new factor.
Step 3 Round the new factor to five decimal places.
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a publicly accessible website, in whole or in part.

27. Creating Present Value Table Factors for Periods Beyond the Table Example
Calculate a new table factor and find the present value of $8,500, if the interest rate is 6% compounded quarterly, for 10 years.
Interest rate per period = 6% ÷ 4 =
1.5%
Compound periods =  4 = 40
1.5%, 20 periods =
.74247
1.5%, 20 periods = 
1.5%, 40 periods =
New table factor (rounded)=  8,500
Present value of $8, = $4,685.71
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a publicly accessible website, in whole or in part.

28. Calculating the Present Value of a Future Amount by Using the Present Value Formula
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a publicly accessible website, in whole or in part.

29. For SOLVING THE PRESENT VALUE FORMULA
Step 1 Add the 1 and the interest rate per period, i.
Step 2 Raise the sum from Step 1 to the nth power by using the yx key on your calculator.
Step 3 Divide the compound amount, A, by the answer from step 2.
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a publicly accessible website, in whole or in part.

30. Chapter Review Problem 1
A firm is planning to build five homes, each costing $125,000, in 2 ½ years. The bank pays 6% interest compounded semiannually. How much should the firm invest now to have sufficient funds to build the homes in the future?
Amount needed =
Interest rate per period =
Compound periods =
Present value =
125,000  5 =
$625,000
6% ÷ 2 = 3%
2.5  2 = 5
 625,000 =
$539,131.25
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a publicly accessible website, in whole or in part.

31. Chapter Review Problem 2
As a savings plan for college, a family deposited $10,000 in an account paying 8% compounded annually when their son was born. How much will the account be worth when their son is 18 years old?
Interest rate per period =
Compound periods =
Present value =
8% ÷ 1 = 8%
18  1 = 18
 10,000 =
$39,960.20
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a publicly accessible website, in whole or in part.

32. Chapter Review Problem 3
A firm deposited $500,000 in an account earning 12% compounded monthly to pay for the future construction of a warehouse. How much will be available for the project in 2 ½ years?
Interest rate per period = 12% ÷ 12 = 1% 30
Compounding periods = 2.5  12 =
1%, 15 periods =
1%, 15 periods = 
30 periods
Rounded new table value =
Amount deposited =  500,000
Compounded amount = $673,925.65
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a publicly accessible website, in whole or in part.

33. Chapter Review Problem 4
A bank is offering a 6-year certificate of deposit (CD) at 4% interest, compounded quarterly. What is the annual percentage yield for an investment of $8,000?
Interest rate per period =
Compound periods =
Compound amount =
Compound interest =
4% ÷ 4 = 1%
1  4 = 4
 8,000 =
$8,324.80
8, – 8,000 =
$324.80
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a publicly accessible website, in whole or in part.