# Draw a timeline for (1) a \$100 lump sum cash flow at the end of year 2, (2) an ordinary annuity of \$100 per year for 3 years and (3) an uneven cash flow stream of -\$50, \$100, \$275, and \$50 at the end of years 0 through 3.

1. Draw a timeline for (1) a \$100 lump sum cash flow at the end of year 2, (2) an ordinary annuity of \$100 per year for 3 years and (3) an uneven cash flow stream of -\$50, \$100, \$275, and \$50 at the end of years 0 through 3.
2. Calculate the following:
3.  Future value of an initial \$100 after 3 years assuming annual interest of 10%.
4.  Present value of \$100 to be received in 3 years if the discount rate is 10%.
• If a company’s sales are growing at a rate of 20% per year, how long will it take for  the sale to double?
• In order for an investment to double in 3 years, what interest rate must it earn?
• Using a timeline, show examples of an ordinary annuity and an annuity due.
• Calculate the future value of a 3-year ordinary annuity of \$100 if the interest rate is 10%.
• Calculate the present value of a 3-year ordinary annuity of \$100 if the discount rate is 10%.
• Redo calculations for steps 6 and 7 assuming an annuity is due.
• Calculate the present value of an uneven cash flow stream of \$100 at the end of year 1, \$300 at the end of year 2, \$300 at the end of year 3, -\$50 at the end of year 4 assuming a discount rate of 10%.
• Calculate the future value of \$100 after 5 years under 12% annual compounding,  semiannual compounding, quarterly compounding, and monthly compounding.
• Calculate the effective rate of interest for a nominal rate of 12% compounded semiannually, quarterly, and monthly.
• Will the effective rate ever equal the nominal rate? Explain your answer.