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# Choice between four retirement annuities.

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P3-41. Jill Chew wishes to choose the best of four immediate retirement annuities available to her. In each case, in exchange for paying a single premium today, she will receive equal annual end-of-year cash benefits for a specified number of years. She considers the annuities to be equally risky and is not concerned about their differing lives. Her decision will be based solely on the rate of return she will earn on each annuity. The key terms of each of the four annuities are shown in the following table.

Annuity Premium Paid Today Annual Benefit Life (years)

A \$30,000 \$3,100 20
B 25,000 3,900 10
C 40,000 4,200 15
D 35,000 4,000 12

a. Calculate to the nearest 1 percent the rate of return on each of the four annuities Jill is
considering.

b. Given Jill's stated decision criterion, which annuity would you recommend?

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\$2.19

## Time Value of Money questions (Future Value, Annuity) , Yield to Call of bonds

1) Terry Austin is 30 years old and is saving for her retirement. She is planning on making 36 contributions to her retirement account at the beginning of each of the next 36 years. The first contribution will be made today (t = 0) and the final contribution will be made 35 years from today (t = 35). The retirement account will earn a return of 10 percent a year. If each contribution she makes is \$3,000, how much will be in the retirement account 35 years from now (t = 35)?
\$894,380
\$813,073
\$897,380
\$987,118
\$978,688

2) Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday. She is saving money today for her retirement and is establishing a retirement account with your office. She would like to withdraw money from her retirement account on her birthday each year until she dies. She would ideally like to withdraw \$50,000 on her 85th birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw \$73,205 on her 89th birthday). She plans to die on her 90th birthday, at which time she would like to leave \$200,000 to her descendants. Your client currently has \$100,000. You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years.

Your client plans to contribute an equal amount of money each year until her retirement. Her first contribution will come in 1 year; her 10th and final contribution will come in 10 years (on her 85th birthday). How much should she contribute each year to meet her objectives?
\$12,401.59
\$12,998.63
\$13,243.18
\$13,759.44
\$14,021.53

3) A corporate bond which matures in 12 years, pays a 9 percent annual coupon, has a face value of \$1,000, and a yield to maturity of 7.5 percent. The bond can first be called four years from now. The call price is \$1,050. What is the bond's yield to call?
6.73%
7.10%
7.50%
11.86%
13.45%