Wetzel
Math 110
4.6 - Exponential Growth and Decay
Compound Interest Problem -
Ex.:
1.) You inherit $20,000 and invest it at 6.5% interest compounded semi-annually. Complete the table below to find how much interest was earned after t years.
|
Years, t |
Total Amount |
Interest Earned |
|
5 |
|
|
|
10 |
|
|
|
15 |
|
|
|
20 |
|
|
|
40 |
|
|
Note: The larger n is, the more interest earned.
What if n was infinitely large? $1 is invested at 100% interest for 1 year compounded n times.
|
n |
|
|
|
1 |
2 |
|
|
5 |
2.4883 |
|
|
10 |
2.5937 |
|
|
100 |
2.7048 |
|
|
1000 |
2.7169 |
|
|
10,000 |
2.7182 |
This is e.
Continuous Compound Interest Problem -
Ex.:
2.) If the same $20,000 was invested at 6.5% interest compounded continuously, how much would be in the account after 20 years? How much interest was earned?
Depreciation –
Ex.:
3.) Instead of investing the $20,000 you inherited, you decide to buy a new car. A vehicle depreciates at 30% a year. Complete the table below to find how much the car is worth after t years.
|
Years, t |
Car Value |
|
|
1 |
|
|
|
2 |
|
|
|
3 |
|
|
|
4 |
|
|
|
5 |
|
|
HW: 6th Ed. p.440 #1, 3, 13, 15, 19-23odd, 45
5th Ed. p.430 #1, 3, 7-11odd, 15, 21, 29
