a. Derive the formula for the future value of an ordinary annuity with $1 payments, 20 payment periods, and 5% interest per payment period, exactly as we did in class:

The bottom equation written here is just a statement of the future value of the ordinary annuity (written based on the bucket approach, as usual), while the top equation is the result of multiplying both sides of the bottom one by 1.05. Write out the left side of the top equation, then subtract the bottom equation from the top one, and use the results to solve for FV.

= (1.05)FV

($1)(1.05)¹⁹ + ($1)(1.05)¹⁸ + + ($1)(1.05)³ + ($1)(1.05)² + ($1)(1.05) + $1 = FV __________________________________________________________________________________

b. Now do the same, on your own, to derive the formula for the future value of an ordinary annuity with $1 payments, 30 payment periods, and 4% interest per payment period.