Day 15 – Continuously Compounded Interest and Natural Logs



Day 15 – Continuously Compounded Interest and Natural Logs

Thinking Skill: Focus on the task for long periods of time.

You invest $6000 at an 8% annual rate. At the end of 5 years, how much do you have if the interest is compounded:

a) 1 time per year

b) semi-annually (two times per year)

c) quarterly (4 times per year)

d) monthly

e) daily

f) What if interest was compounded CONTINUOUSLY? In other words, the interest that you are earning is constantly being added to your principal? There is a formula for compound interest:

A= P= r = t =

What is e?

e is the base of a ________________________________________, written _____________.

It has the value, rounded to the nearest thousandth, of _______________.

(Similar to [pic], it is a decimal that does not terminate or repeat.)

When we write y = ln x it means the same thing as: _______________________________.

Evaluate/Simplify each of the following (no calculator required):

1. [pic] 2. [pic] 3. [pic] 4. [pic]

Find these on a calculator (rounded to 3 places): 5. [pic] 6. [pic]

Use the Continuous Compounded Interest Formula, [pic], to answer these questions:

1. You invest $5000 at 6.3% compounded continuously for 7 years. How much do you have?

2. You invest $2750 at 3.99% compounded continuously for 3 years. How much do you have?

3. You invest $4000 at 6.3% compounded continuously. AFTER HOW MANY YEARS (to the nearest tenth), will you have $8500?

Calculator Method: Equation Method:

4. You invest $32,500 at 3.99% compounded continuously. AFTER HOW MANY YEARS (to the nearest tenth), will you have $50,000?

Calculator Method: Equation Method:

5. You invest $10,00 at 8.25% compounded continuously. AFTER HOW MANY YEARS (to the nearest tenth), will you triple your money?

Calculator Method: Equation Method:

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Continuously Compounded Interest Formula:

[pic]

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