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Applications Growth and Decay Math of FinancePowerPoint Presentation

Applications Growth and Decay Math of Finance

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Applications Growth and Decay Math of Finance

ApplicationsGrowth and DecayMath of Finance

Lesson 2.6

- If Y0 is the initial quantity present
- The amount present at time t is

- This is continuous growth/decay
- Contrast to periodic growth/decay

- Convert between, knowing b = ek
- Result is k ≈ r (recall that b = 1 + r)

- Given growth data, determine continuous growth function
- Initial population = 2500
- Ten years later, population is 4750
- Assuming continuous growth, what is function

- Strategy
- What is y0?
- Use (10,4750), solve for k
- Write function

- For exponential decay
- Recall that 0 < b < 1 and r < 0
- That means k < 0 also

- Suppose Superman's nemesis, Kryptonite has half life of 10 hours?
- How long until it reaches 30% of its full power and Superman can save the city?

- Strategy
- Again, find k using .5 and 10
- Then find t using the .3

For continuous compounding

- Given
- r is stated annual rate
- m is number of compounding periods

- Then effective rate of interest is
- Try it … what is effective rate for 7.5% compounded monthly?

For continuous compounding

- Consider the formula for compounded interest
- Suppose we know A and need to know P
- This is called the "present value"

- Try it out …
- Find the present value of $45,678.93 if …
- Interest is 12.6%
- Compounded monthly for 11 months

- Lesson 2.6A
- Page 133
- Exercises 7 – 39 odd

- Lesson 2.6B
- Page 133
- Exercises 16, 18, 20, 22, 41, 43, 45, 47