Chapter 5.6, Problem 13E

In Exercises 13-16, use the Annual Payout Annuity with COLA Formula to find the deposit necessary to receive monthly payouts with an annual cost-of-living adjustment. To use the formula, all figures must be annual figures including the payout and the annual rate. You can adapt the formula for monthly payouts by using

• The future value of a one-year ordinary annuity in place of the annual payout, where pymt is the monthly payout, and

• The annual yield of the given compound interest rate in place of the annual rate $r$

Fabiola Macias is about to retire, so she is setting up a payout annuity with her bank. She wishes to receive a monthly payout for the next twenty-five years, where the payout starts at $\$1,000$ per month and receives an annual COLA of $3\%$. Her money will earn $10\%$ compounded monthly.

a. The annual payout is the future value of a one-year ordinary annuity. Find this future value.

b. The annual rater is the annual yield of $10\%$ interest compounded monthly. Find this annual yield. (Do not round it off)

c. Use the Annual Payout Annuity with COLA Formula to find how much money she must deposit.

d. Fabiola could have saved for her payout annuity with an ordinary annuity. If she had started doing so thirty years ago, what would the required monthly payments have been? (The two annuities pay the same interest rate.)