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hotpotato |
07/06/05 |
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 divide by 2 .05568 average
c) present value annuity = c * [1-1/(1+r)^t]/r
where c = payment = 200/month = 2400 / year
PVA = 2400 x [1-(1/(1.05)^7] /.05
=2400 x (1-.71068) / 0.05
= 13887.36
FV of lump sum
13887.36 x (1.05)^7 = 19540.91013
future value of new annuity:
FVA = C x [(1 + r)^t - 1]/r
4800 x (1.06136)^28 / (.06136)
= 414487.9775
invest 400/month = 4800 a year
age 60 retirement
60 - year 32 = 28 years
d) Present value annuity = C x [1-(1/(1 +r)]/r
=27300 (525 x 52)
27300 x [1 - (1/(1.05568)^20]/.00568
=27300 x 11.88326
=324413.0388
im not sure how you would do d. can you please check if my above
answers are correct. Thank you so much! |
Clarification/Follow-up by hotpotato on 07/07/05 12:17 pm:
for part c) she can save 400 a month compounded quarterly from restarting to retirement therefore future value annuity
i need to know the original annuity growth after contributions stop
2) future value of lump sum
3. future value of new annuity
part d) she wants to collect 545 per month for 20 years
putting c) and d) below in numbers
c) present value annuity = c * [1-1/(1+r)^t]/r
where c = payment = 200/month = 2400 / year
PVA = 2400 x [1-(1/(1.05)^7] /.05
=2400 x (1-.71068) / 0.05
= 13887.36
FV of lump sum
13887.36 x (1.05)^7 = 19540.91013
future value of new annuity:
FVA = C x [(1 + r)^t - 1]/r
4800 x (1.06136)^28 / (.06136)
= 414487.9775
invest 400/month = 4800 a year
age 60 retirement
60 - year 32 = 28 years
d) Present value annuity = C x [1-(1/(1 +r)]/r
=27300 (525 x 52)
27300 x [1 - (1/(1.05568)^20]/.00568
=27300 x 11.88326
=324413.0388
FV of lump sum 19540.91013 + FV of new annuity = 414487.9775
=434028.8876
Current savings: 434028.8876 - need for future income: 324413.0388 =
109615.8488
the cost of the trip is 5000 + present value of my future interest
payments
PVA = 5000 x [1 - 1/(1 + r)^t]/r
rates for two =0.293333 + 0.27443 from the EAR from part a, b, =
.56776
using first rate:
5000 x [1 - 1/(1.29333) ^4]/.29333
= 10953.36311 as my final answer.
can you let me know if i'm doing it right? thank you!
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