mac1105_lecture25_1

mac1105_lecture25_1 - L25 Applications of Exponential...

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270 L25 Applications of Exponential Functions; Logistic Models Simple Interest Formula: If a principal of P dollars is invested for a period of t years at a per annum interest rate R , expressed as a decimal, the interest I earned is IP R t = ⋅⋅ The interest I is called the simple interest . Compound interest is the interest paid on principle and previously earned interest. Compound Interest Formula : The amount A after t years due to a principal P invested at an annual interest rate r compounded n times per year is 1 nt r AP n ⎛⎞ =⋅ + ⎜⎟ ⎝⎠ Note : The more frequently the interest rate is compounded (the larger n ), the larger is the amount of A. Question : Is it true that A →∞ , as n ?
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271 Example : Suppose that a principal P = $1.00 is invested at an annual interest rate 1 r = (100%) compounded n times per year. (a) Find the future value A after 1 t = year. (b) What value does A approach when n →∞ ? In general, lim 1 nt rt n r P Pe n →∞ ⎛⎞ += ⎜⎟ ⎝⎠ Continuous Compounding: The amount A after t years due to a principal P invested at an annual interest rate r compounded continuously is rt A Pe =
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272 Example : If $5,000 is deposited in an account at an interest rate 6%, how much will be in the account after 10 years if (a) compounded quarterly (b) compounded continuously?
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273 Example : How long will it take for $500 to grow to $6000 at an interest rate of 10% per annum if interest is compounded (a) daily (b) continuously
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mac1105_lecture25_1 - L25 Applications of Exponential...

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