1. Compound Interest

2. Compound Interest and Present Value

3. Compound Interest and Present Value
Learning Unit Objectives
Compound Interest (Future Value) – The Big Picture
Compare simple interest with compound interest
Calculate the compound amount and interest manually.
Explain and compute the effective rate

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. 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

6. 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
Compounding fortnightly Every two weeks

7. 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 3 years at 6% annually, semiannually, or quarterly What is N and R?
Periods
Rate
Annually: 6% / 1 = 6%
Semiannually: 6% / 2 = 3%
Quarterly: 6% / 4 = 1.5%
Annually: 3 x 1 = 3
Semiannually: 3 x 2 = 6
Quarterly: 3 x 4 = 12

8. Simple Versus Compound Interest
Compounded
Al Jones deposited $1,000 in a savings account for 5 years at an annual interest rate of 10%. What is Al’s simple interest and maturity value?
Al Jones deposited $1,000 in a savings account for 5 years at an annual compounded rate of 10%. What is Al’s interest and compounded amount?
I = P x R x T
I = $1,000 x .10 x 5
I = $500
Amount of money = $1,000 + $500
= $1,500
Interest: $1, $1,000 = $610.51

9. 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

10. - Future Value of $1 at Compound Interest

11. Calculating Compound Amount by Table Lookup
Steve Smith deposited $6,000 in a savings account for 5 years at an semiannual compounded rate of 10%. What is Steve’s interest and compounded amount?
N = 5 x 2 = 10
R = 10% = 5% 2
Table Factor =
Compounded Amount:
$6,000 x = $9,773.40
I = $9, $6,000 = $3,773.40

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

13. Compounding Interest Daily
Calculate what $2,000 compounded daily for 7 years will grow to at 6%pa
T = 7 years
R = 6%
A=P(1+r)n
=$2,000 ( )7= $3,007.3