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1. FINDING THE REQUIRED INTEREST RATE Your parents will retire in 19 years. They currently have $350,000 saved, and they think they will need $800,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?

2. TIME TO REACH A FINANCIAL GOAL You have $33,556.25 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $220,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal?

3. PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM An investment will pay $150 at the end of each of the next 3 years, $250 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 11% annually, what is its present value? Its future value?

4. PRESENT AND FUTURE VALUES FOR DIFFERENT INTEREST RATES Find the following values. Compounding/discounting occurs annually.

a. An initial $200 compounded for 10 years at 4%

b. An initial $200 compounded for 10 years at 8%

c. The present value of $200 due in 10 years at 4%

d. The present value of $1,870 due in 10 years at 8% and at 4%

e. Define present value and illustrate it using a time line with data from part d. How are present values affected by interest rates?

5. FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS Find the amount to which $500 will grow under each of these conditions:

a. 12% compounded annually for 5 years

b. 12% compounded semiannually for 5 years

c. 12% compounded quarterly for 5 years

d. 12% compounded monthly for 5 years

e. 12% compounded daily for 5 years

f. Why does the observed pattern of FVs occur?