1. 3.10 & 3.11
Exponential Growth
Obj: apply compound and continuously compounding
interest formulas

2. What an Offer!!
Suppose that the local bank offered an incredible deal, a100% APR savings account, but only for one year. Obviously you would want to put all of your money into it, but let’s say that you have $100 to invest. How much would you have at the end of the year? It depends on how often the interest is compounded.

3. How much would you have if the interest was compounded…
Annually?
$200
Semi-annually?
$225
Quarterly?
$244.14
Monthly?
$261.30

4. What if it were compounded more often?
Weekly?
$269.26
Daily?
$271.46
Hourly?
$271.81
Does there seem to be a limit?

5. Find the limit…
f(102) = f(104) = f(106) = Do you recognize it?

6. Interest Formulas Compound Interest Formula
p = principal r = interest rate n = compounding period t = time
Continuously Compounding Interest Formula

7. Practice
Robin invests $1200 at 6% APR and wants to know what happens as interest is compounded more and more often. Find to the nearest cent the balance of Robin’s account at the end of one year if interest is compounded a. Biannually b. Monthly c. Weekly d. Daily

8. Practice
You put $2000 into a savings account that earns 5% APR compounded continuously.
How much money will you have after 2 years? 5 years?
How long will it take for your money to double?