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# Pre-Cal 40S April 27, 2009

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More on the number e, natural logarithms, and compound interest.

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### Pre-Cal 40S April 27, 2009

1. 1. THE Exponential Function exponential function - quot;equot; by ﬂickr user jeff_boy50
2. 2. A = AMOUNT of money at the end of the term P = PRINCIPLE amount, the amount originally invested or borrowed r = RATE of interest as a decimal number n = NUMBER of times the principle is compounded per year t = TIME in years Time Principle Rate Interest Balance
3. 3. Who wants to be a millionaire? What is compound interest? How does this formula quot;workquot;? How much money will you have after 5 years if you invest \$300.00 at 6% interest compounded annually? monthly?
4. 4. The number e ... e= ... Source: e to 1 000 000 digits
5. 5. The Exponential Function The Natural Logarithm
6. 6. Who wants to be a millionaire? It turns out that when interest is compounded continuously, we use this formula to calculate the total value of the amount, A, earned on the principal, P, after any period of time, t. How much money will you have after 5 years if you invest \$300.00 at 6% interest compounded continuously? If you invest \$300.00 at 6% interest compounded continuously how long will it take to double your money?
7. 7. The Rule of 72 Here's a handy way to ﬁgure out how long your investment will take to double in value. It is called the Rule of 72. (Interest Rate %) x (Years to Double) = 72 To ﬁnd the number of years given a percentage: Years = 72 (Interest Rate %) To ﬁnd the percentage required to double given the years: Rate = 72 Years Numbers 72 by ﬂickr user szczel
8. 8. Solve ...
9. 9. Solve ...