Pg. 282 Homework Worksheet#4 – 6 Pg. 268#15 – 18, 29, 41, 47 – 49 #1 6% quarterly#28.25% monthly #3 7.20% daily#48.5% quarterly #5 $36,013.70#6$13,937.28.

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Pg. 282 Homework Worksheet#4 – 6 Pg. 268#15 – 18, 29, 41, 47 – 49 #1 6% quarterly#28.25% monthly #3 7.20% daily#48.5% quarterly #5 $36,013.70#6$13, #7 x = $749.35#15R = $ #16 R = $151.62#17R = $ #18 R = $1,032.14

5.3 Effective Rates and Annuities Effective Annual Rate The effective annual rate basically is an equation that breaks down a percentage and compounding into uniformed terms, so you can easily compare two and see which will yield better results. Effective Annual Rate = i eff of APR r compounded k times per year. Ordinary Annuity An ordinary annuity is a sequence of equal regular periodic payments to be made in the future. Future Value is like when people invest into a retirement account. Present Value is like when people make mortgage or car payments.

5.3 Effective Rates and Annuities Examples: Compare the effective annual rates of an account paying 8.75% compounded quarterly with an account paying 8.75% compounded monthly. Sarah makes quarterly payments of $500 into a retirement account that pays 8% compounded quarterly. How much will be in Sarah's account at the end of 25 years?

5.3 Effective Rates and Annuities Examples What monthly payments are required for a 5 – year, $9,000 car loan at 12.5% APR compounded monthly? Solve the following equation for i using a graphing utility. Explain how this problem relates to a car loan of $10,000 requiring monthly payments of $200.

5.3 Effective Rates and Annuities A building, item of equipment, or other capital improvement investment that a business might make has a useful life. The item depreciates from the time it is new (original cost C) until it reaches the end of its useful life (salvage value S). A continuous model for book value B at any time t using the constant percentage method: B = C(1 – r) t where S = C(1 – r) n, 0 ≤ t ≤ n

5.3 Effective Rates and Annuities Suppose a machine costing $17,000 has a useful life of 6 years and a salvage value of $1,200. – Assume that the machine is depreciated using the constant percentage method to find r. – Draw a complete graph of the book value. – What values of t make sense? – What is the book value in 4 years and 3 months?