Reply
Wed 6 Jul, 2005 01:28 pm
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!
Your third rate is not .11136 percent. If you have two different accounts, your average would be half of the .11136 percent annual return. Also, it is impossible to predict future long-term interest rates. CD and bond rates change almost daily. It is impossible to forecast future stock performance. The best you can do is to prepare an estimate between several different scenarios - a best case and worst case rates of return.
Assuming that the interest rates are fixed for the term of your problem, I have calculated a) the $200/month for 7 years, b) $4800/year for 25 years, c) the combined total for a and b, and d) the amount of funds available for withdrawal for 21 years (from age 60 to age 80 with the average rate of return for the retirement years.
a) total value at age 59 $ 80,432.67. Interest on this account continues to accumulate until retirement at 5 percent.
b) total value at age 59 $284,938.36.
c) combined value of a and b $ 365,371.03
d) withdrawal from age 60 to 80 (21 years) assuming rate of interest at (.05 + .061364/2) .055682 is $28,360.59.
One note of caution: Fixed rate of withdrawal is not a good idea for retirement, because it doesn't take into consideration the inflation rate.
There is a balance of $ .04c.
finance
thank you for your help, can you show me the steps and formulas of how you got the answers. That would really help me. Thank you thank you !
Stumble It!
Tweet This
Bookmark on Delicious
Share on Facebook
Share on MySpace