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Section 6.7 – Financial Models Simple Interest Formula Compound Interest Formula Continuous Compounding Interest Formula

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Section 6.7 – Financial Models Example - Simple Interest Examples - Compound Interest What is the future value of a $34,100 principle invested at 4% for 3 years $21,000 is invested at 13.6% compounded quarterly for 4 years. What is the return value? The amount of $12,700 is invested at 8.8% compounded semiannually for 1 year. What is the future value?

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Section 6.7 – Financial Models Examples - Compound Interest Example - Continuous Compounding Interest If you invest $500 at an annual interest rate of 10% compounded continuously, calculate the final amount you will have in the account after five years. How much money will you have if you invest $4000 in a bank for sixty years at an annual interest rate of 9%, compounded monthly?

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Effective Interest Rate – the actual annual interest rate that takes into account the effects of compounding. Section 6.7 – Financial Models Which is better, to receive 9.5% (annual rate) continuously compounded or 10% (annual rate) compounded 4 times per year? Continuous compounding Compounding 4 times per year

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Present Value – the initial principal invested at a specific rate and time that will grow to a predetermined value. Section 6.7 – Financial Models How much money do you have to put in the bank at 12% annual interest for five years (a) compounded 6 times per year and (b) compounded continuously to end up with $2,000? Continuous compoundingCompounding 6 times per year

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Example Section 6.7 – Financial Models What rate of interest (a) compounded monthly and (b) continuous compounding is required to triple an investment in five years?

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Uninhibited Exponential Growth Section 6.8 – Exponential Growth/Decay Models; Newton's Law of Cooling and Logistic Growth/Decay Models Uninhibited Exponential Decay

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Examples Section 6.8 – Exponential Growth/Decay Models; Newton's Law of Cooling and Logistic Growth/Decay Models The population of the United States was approximately 227 million in 1980 and 282 million in 2000. Estimate the population in the years 2010 and 2020. Find k 2020 2010

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Examples Section 6.8 – Exponential Growth/Decay Models; Newton's Law of Cooling and Logistic Growth/Decay Models A radioactive material has a half-life of 700 years. If there were ten grams initially, how much would remain after 300 years? When will the material weigh 7.5 grams? Find k or 300 years or 7.5 grams

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Newton’s Law of Cooling Section 6.8 – Exponential Growth/Decay Models; Newton's Law of Cooling and Logistic Growth/Decay Models

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Newton’s Law of Cooling Section 6.8 – Exponential Growth/Decay Models; Newton's Law of Cooling and Logistic Growth/Decay Models Example A pizza pan is removed at 3:00 PM from an oven whose temperature is fixed at 450 F into a room that is a constant 70 F. After 5 minutes, the pizza pan is at 300 F. At what time is the temperature of the pan 135 F? Find k t @ 135 F

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Logistic Growth/Decay Section 6.8 – Exponential Growth/Decay Models; Newton's Law of Cooling and Logistic Growth/Decay Models

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Logistic Growth/Decay Section 6.8 – Exponential Growth/Decay Models; Newton's Law of Cooling and Logistic Growth/Decay Models Example 2000 2005 P(t) = 85%

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