1. 5.4 5.4 – The Number e and the Function e x Objectives: You should be able to… 1. Use compound interest formulas to solve real-life problems.

2. Compound Interest To examine compound interest at different interest periods we use the formula where i is the rate (expressed as a decimal), n is the period, and t is years it will grow to an amount A of the principal P.

3. For interest compounded continuously, we can use… P(t) = P 0 e rt where P 0 is the initial amount, r is the annual rate, and t is the time in years. **NOTE** this formula can be used for any quantity compounding continuously.

4. Evaluate: a) e – 0.06 b) Example:

5. Suppose you invest $1.00 at 12% annual interest. Calculate the amount that you would have after one year if the interest is compounded: a) quarterly b) monthly c) continuously Example:

6. With which plan would an investor earn more, Plan A, B, or C? Plan A: A 7.5% annual rate compounded monthly over a 4-year period. Plan B: A 7.2% annual rate compounded daily over a 4- year period. Plan C: A 7% annual rate compounded continuously over a 4-year period.

7.  Effective Annual Yield – If semiannual is 4%, you cannot multiply by 2 for EAY because you wouldn’t be considering the interest earned in the first period.

8. 100 deposited in a bank account that compounds interest quarterly yields $107.50 over 1 year. Find the effective annual yield. Example:

9. Look at graph of y = e x. a. Graph y = e x + 1. b. Graph y = e x + 1. Example: