1. Continuous Interest MAT 112

2. How Frequent?

3. How many periods?

4. Construct a new formula

5. A Little Math Trick

6. As m gets large...

7. Call it “e”

8. Continuous Compound Interest Note that here the exponent is “ rt ”, NOT “ mt ” as in the earlier formula.

9. 12%, compounded continuously

10. Compare

11. Continuous Interest CERTIFICATES OF DEPOSIT TermInterest Rate%APY 3 Months up to 6 Months*1.781.80 6 Months up to 1 Year*2.082.10 1 Year up to 2 Years*2.322.35 2 Years up to 4 Years*2.963.00 4 Years up to 5 Years*3.924.00 * $500.00 Minimum Opening Deposit Interest is Compounded Continuously, credited monthly. Penalty for early withdrawal. http://www.hudsonriverbank.com/current_rates_sav.htm

12. Example

13. Another Example

14. Solving an equation If not algebraically, then let’s try solving it graphically.

15. Finding the intersection Graph both sides of the equation and see where they’re equal. Procedure for approximating the point of intersection.

16. Finding the intersection The balance reaches $6000 at around 9.9 years.

17. When compounded monthly… For an account earning 8% compounded monthly, how long does it take for a deposit of $10000 to increase to a balance of $16000? Graph it and solve.

18. When compounded monthly… After 5.89 years (5 years, 11 months), the account has reached $16000.