1. Compound Interest Money, where fashion begins…

2. Vocabularies and Symbols A = Accumulated Amount (ending balance, in $) A = Accumulated Amount (ending balance, in $) P = Principle (beginning balance, in $) P = Principle (beginning balance, in $) r = Interest Rate (such as 5%, or 0.05) r = Interest Rate (such as 5%, or 0.05) t = Time (in years) t = Time (in years)

3. Simple Interest: An 100$ deposit is earning 10% annual simple interest in a saving account. What will be the ending balance after t years, for t = 0, 1, 2, 3 and 4 years? An 100$ deposit is earning 10% annual simple interest in a saving account. What will be the ending balance after t years, for t = 0, 1, 2, 3 and 4 years? A(0)=100 A(0)=100 A(1)=110 A(1)=110 A(2)=120 A(2)=120 A(3)=130 A(3)=130 A(4)=140, etc… A(4)=140, etc… Every year, the amount of interest is a constant 10$, which is 10% of P. Every year, the amount of interest is a constant 10$, which is 10% of P.

4. Simple vs. Compound Interest SimpleCompound A(0)=100A(0)=100 A(1)=110A(1)=110 A(2)=120A(2)=121 A(3)=130A(3)=133.1 A(4)=140A(4)=146.41

5. Compound Interest A = Accumulated Amount A = Accumulated Amount P = Principle P = Principle r = Interest Rate r = Interest Rate t = Time t = Time

6. Compound Interest A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: Simple Interest Compounded Annually Compounded Quarterly

7. Compound Interest A = Accumulated Amount A = Accumulated Amount P = Principle P = Principle r = Interest Rate r = Interest Rate t = Time t = Time n = Compounding Frequency (# of times a year. If annually, n=1; if quarterly, n=4, etc.) n = Compounding Frequency (# of times a year. If annually, n=1; if quarterly, n=4, etc.) Note: Note: nt = total # of compounding periods r/n = interest rate earned in each compounding period

8. Compound Interest A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: Simple Interest Compounded Annually Compounded Quarterly Compounded Monthly Compounded Daily

9. Continuously Compound A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: Compounded CONTINUOUSLY Compounded CONTINUOUSLY

10. Continuously Compounded Interest A = Accumulated Amount A = Accumulated Amount P = Principle P = Principle r = Interest Rate r = Interest Rate t = Time t = Time

11. Continuously Compound A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: Compounded CONTINUOUSLY Compounded CONTINUOUSLY

12. Compound Interest A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: Simple Interest:$3125 Compounded Annually:$3190.70 Compounded Quarterly:$3205.09 Compounded Monthly:$3208.40 Compounded Daily:$3210.01 Compounded Continuously:$3210.06

13. Interest rate vs. Compounding P = $2500 P = $2500 r = 5% r = 5% t = 5 years t = 5 years Compounded daily will give: Compounded daily will give: $3210.01 $3210.01 If compounded annually, but raise interest rate to 5.5%, it will give: If compounded annually, but raise interest rate to 5.5%, it will give: $3267.40 $3267.40 Which is a better deal: compounding more frequently, or raising interest rate?

14. Carb, where fashion deceases… Fin…