Expert: Ed McFarland - 7/6/2005

Question
thank you so much for your fast reply. are my other answers correct?
the third rate in part b is an average? so i should have taken .11136/2?
im a bit confused with c and d, can you please show me. Thank you thank you!

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Followup To
Question -
Hi expert, I have a question to ask you and I want to show you what i have done so I am on the right track. Can you please let me know if i'm doing the right thing?

question:
Anabelle, a single 35 year old teacher is thinking of retiring when she turns 60. When she was 25, she started saving $200 each month in an investment account that earned her 5% per year. After seven years, Anabelle bought a new car and stopped making contributions to her account. However, Anabelle has just finished taking a few extra night classes, and has been promoted to Principal of her school. This means that she can resume her contributions for her retirement.  She now has $400 per month available to invest, but her financial adviser has offered her a return of 6% per year compounded quarterly. In addition, Anabelle was told that her past savings will continue to earn the old rate of return. She thinks that if she can withdraw $525 each week, starting after a week of her retirement, she should be well off as long as she lives.

b)Calculate the three effective periodic rates of return.
c)How much will Anabelle have to save each month after she resumes her retirement savings?
d)If Anabelle expects to live until she is 80 years old, what would your answer be for part c)?

b)
first rate
EPR = [1 + quoted rate/m]^m - 1
[1 + 0.05/1]^1 - 1 = .05000

second rate
[1 + 0.06/4]^4 - 1 = .06136

third rate = 1st rate + second rate
.0500 + .06136
= .11136

c) future value annuity = c * [(1 + r)^t - 1]/r
where c = payment = 200/month = 2400 / year

2400 x [(1.05)^6 - 1]/(0.05)
= 16324.59075

finding the annual rate:
EAR = [1 + quoted rate/m]^m - 1
[1 + 0.06/4]^4 - 1
.06136

invest 400/month = 4800 a year
age 60 retirement
60 - year 32 = 28 years

Present value annuity = 4800 = C x [1-1/(1.06136)^28]/(.06136)
4800 = C x 13.22148
C = 363.04559 is what she has to save

d) im not sure how you would do d. can you please check if my above answers are correct. Thank you so much!
Answer -
Here are the clues to finishing the work:

the third rate in part b is an average.

Part c: She can save $400 monthly that will be compounded quarterly from restarting to retirement, future value of an annuity.

Part d, She wants to collect 525 per month for 20 years, present value of an an annuity. Will the old savings, growing at 5%, combined with new savings you figured out in part c be enough?

Good luck

Answer
I usually don't do homework problems, but I'll try and help you see the light here.

The third part of b is asking the yeild you'd be getting, one pile gets 5% and the other 6.136, you've shown the advntage of quarterly compunding, her savings are getting the average. To be more correct it would be a weighted average but don't bother with that.

When I teach this, I have students graph out the savings and spending. Money on the vertical, cash on the horiziontal

In part c you need to figure out 3 things, the orginal annuity, the its growth after contributions stop, the future value of a lump sum and the future value of the new annuity.

In part d you are asked if what did in part c will keep her from running out of money, the present value of an annuity, 525 paer week for 20 years.

Good luck