1. Compound Interest and Present Value
Chapter 12
Compound Interest and Present Value

2. Learning Unit Objectives
#12
Compound Interest and Present Value
Learning Unit Objectives
Compound Interest (Future Value) – The Big Picture
LU12.1
Compare simple interest with compound interest
Calculate the compound amount and interest manually and by table lookup
Explain and compute the effective rate

3. Learning Unit Objectives
#12
Compound Interest and Present Value
Learning Unit Objectives
LU12.2
Present Value -- The Big Picture
Compare present value (PV) with compound interest (FV)
Compute present value by table lookup
Check the present value answer by compounding

4. Compounding Interest (Future Value)
Compounding - involves the calculation of interest periodically over the life of the loan or investment
Compound interest - the interest on the principal plus the interest of prior periods
Future value (compound amount) - is the final amount of the loan or investment at the end of the last period
Present value - the value of a loan or investment today

5. Compounding Terms Compounding Periods Interested Calculated
Compounding Annually Once a year
Compounding Semiannually Every 6 months
Compounding Quarterly Every 3 months
Compounding Monthly Every month
Compounding Daily Every day

6. Figure 12.1 Future Value of $1 at 8% for Four Periods
Compounding goes from present value to future value
Future Value
After 4 periods $1 is worth $1.36
After 3 periods $1 is worth $1.26
After 2 periods $1 is worth $1.17
After 1 period $1 is worth $1.08
Present
value
$1.2597
$1.3605
$1.1664
$1.08
$1.00
Number of periods

7. Figure 12.1 Future Value of $1 at 8% for Four Periods
Manual Calculation

8. Tools for Calculating Compound Interest
Number of periods (N) Number of years multiplied the number of times the interest is compounded per year
Rate for each period (R) Annual interest rate divided by the number of times the interest is compounded per year
If you compounded $100 for 4 years at 8% annually, semiannually, or quarterly What is N and R?
Periods
Rate
Annually: 4 x 1 = 4
Semiannually: 4 x 2 = 8
Quarterly: 4 x 4 = 16
Annually: 8% / 1 = 8%
Semiannually: 8% / 2 = 4%
Quarterly: 8% / 4 = 2%

9. Simple Versus Compound Interest
Compounded
Simple
Bill Smith deposited $80 in a savings account for 4 years at an annual interest
rate of 8%. What is Bill’s simple interest and maturity value?
Bill Smith deposited $80 in a savings account for 4 years at an annual interest
rate of 8%. What is Bill’s interest and compounded Amount?
I = P x R x T
I = $80 x .08 x 4
I = $25.60
MV = $80+ $25.60
MV = $105.60
Interest: $ $80.00 = $28.83

10. Calculating Compound Amount by Table Lookup
Step 4. Multiply the table factor by the amount of the loan.
Step 3. Go down the period column of the table to the number desired; look across the row to find the rate. At the intersection is the table factor
Step 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 year
Step 1. Find the periods: Years multiplied by number of times interest is compounded in 1 year

11. Calculating Compound Amount by Table Lookup
Pam Donahue deposits $8,000 in her savings account that pays 6% interest compounded quarterly. What will be the balance of her account at the end of 5 years?
N = 4 x 5 = 20
R = 6% = 1.5% 1
Table Factor =
Compounded Amount:
$8,000 x = $10,775.20

12. Nominal and Effective Rates (APY) of Interest
Nominal Rate (Stated Rate) - The rate on which the bank calculates interest.
Truth in
Savings
Law Annual
Percentage
Yield
Effective Rate = Interest for 1 year
(APY) Principal

13. Calculating Effective Rate APY
Blue, 8% compounded quarterly
Periods = 4 (4 x 1)
Percent = 8% = 2% 4
Principal = $8,000
Table 12.1 lookup: 4 periods, 2%
1.0824
x $8,000
Less $8,659.20
$8,000.00
659.20
APY = .0824
$8,000
= 8.24%
Sun, 8% compounded semiannually
Periods = 2 (2 x 1)
Percent = 8% = 4% 2
Principal = $8,000
Table 12.1 lookup: 2 periods, 4%
1.0816
x $8,000
Less $8,652.80
$8,000.00
652.80
APY = .0816
$8,000
= 8.16%

14. Figure 12.3 - Nominal and Effective Rates (APY) of Interest Compared
Beginning Nominal rate Compounding End Effective rate
balance of interest period balance (APY) of interest
Annual
Semiannual
Quarterly
Daily
$1,060.00
$1,060.90
$1,061.40
$1,061.80
6.00
6.09%
6.14%
6.18%
$1,000
+ 6%

15. Compounding Interest Daily
Calculate by Table 12.2 what $1,500 compounded daily for 5 years will grow to at 7%
N = 5
R = 7%
Factor
$1,500 x = $2,128.50

16. Figure 12.4 Present Value of $1 at 8% for Four Periods
Present value goes from the future value to the present value
Future Value
$1.0000
$.9259
Present
value
$.8573
$.7938
$.7350
Number of periods

17. Calculating Present Value by Table Lookup
Step 4. Multiply the table factor by the future value. This is the present value.
Step 3. Go down the period column of the table to the number desired; look across the row to find the rate. At the intersection is the table factor.
Step 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 year
Step 1. Find the periods: Years multiplied by number of times interest is compounded in 1 year

18. Table 12.3 - Present Value of $1 at End Period

19. Comparing Compound Interest (FV) Table 12
Comparing Compound Interest (FV) Table 12.1 with Present Value (PV) Table 12.3
Compound value Table Present value Table 12.3
Table Present Future Table Future Present
Value Value Value Value
x $80 = $ x $ = $80.00
(N = 4, R = 8) (N = 4, R = 8)
We know the present dollar amount and find what the dollar amount is worth in the future
We know the future dollar amount and find what the dollar amount is worth in the present

20. Calculating Present Value Amount by Table Lookup
Rene Weaver needs $20,000 for college in 4 years. She can earn 8% compounded quarterly at her bank. How much must Rene deposit at the beginning of the year to have $20,000 in 4 years?
N = 4 x 4 = 16
R = 8% = 2% 4
Table Factor = .7284
Compounded Amount:
$20,000 x = $14,568
Invest
Today