1. Exponential Growth in Finance Math 150
Compound Interest
Exponential Growth in Finance
Math 150

2. Compounding n times per year
Interest computed n times per year
Start with an amount A
After t years, you have
Note that A is increase by multiplication with powers of something slightly bigger than 1

3. Increasing n As n gets larger, the accumulated interest increases
Example: A bank pays 6% interest on a savings account, compounded monthly. What is the value of $1000 after 1 year?
Solution:

4. Credit Card Interest
Example: A bank charges 6% interest per year on a credit card, compounded daily. How much is due on $1000 after one year of interest.
Solution:

5. The Difference .15 per year
Not a whole lot, right? Multiply that times 10,000,000 customers and it works out to $1,500,000 per year in revenue
What if you make payments monthly? Better right? Maybe.

6. Paying Off Credit Cards
How much will you end up paying for a $1000 purchase at 6% per year compounded daily if you pay $100 per month?
Solution:

7. Making Minimum Payments
Pay $20 per month instead

8. Compounding More Often
What if n =1000? ?
What happens to (1+r/n)nt when n gets large
Use r=.06 and t=1 and try it for yourself
(1+.06/n)n

9. Continuously Compounded
As n !1 , (1+r/n)nt becomes ert, so our formula becomes