Pg. 282 Homework

• Worksheet#4 – 6 Pg. 268 #15 – 18, 29, 41, 47 – 49

• #1 6% quarterly #2 8.25% monthly• #3 7.20% daily #4 8.5% quarterly• #5 $36,013.70 #6 $13,937.28• #7 x = $749.35 #15 R = $230.43• #16 R = $151.62 #17 R = $884.61• #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 = ieff 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.

1 1k

eff

ri

k

1 1ni

S Ri

1 1n

iS R

i

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.

601 1

10,000 200i

i

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?