Superfund problem

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smudge

New member
Joined
Mar 5, 2009
Messages
8
Hi
I'm having problems with the calculations for the following question.

Mary is 40 years old today and plans to work until her 65th birthday and then retire, anticipating that she will need sufficient savings to support her until she is 85 years old. (The average life expectance of females in Australia is 81.) Mary believes she will need an annual income of $45,000 during retirement to maintain her life style. She currently earns $54,000 and her employer contributes 9% pa to a superfund whose long term earning rate is 5.4%. On retirement Mary intends to leave her investment in the superfund and draw funds as required.
i. How much will Mary need in the fund on her 65th birthday, given annual withdrawals of $45,000 (20 withdrawals) the first on her 65th birthday, such that there is nothing left in the fund on her 85th birthday?
ii. If Mary currently has $60,000 in her fund and her employer contributes annually as described above with the next contribution on her 41st birthday and the last on her 65th birthday, how much will the fund be worth on her retirement?
iii. How much extra does Mary have to contribute on an annual basis, to meet the target on her 65th birthday (as determined in (a) above)?
iv. If Mary contributes $1,000 for the next 10 years and $3,000 for the remaining 15 years, will she still meet her target?

My workings thus far
i.
PV Annuity Due $45000(1-(1.054/0.054)^-19) +1
= $571539.13

ii.
9% *$54000 = $4860
Future Value of Fund = ($60000+$4860) (1.054)^25
=$241541.75

iii. ??? $571539.13-$241541.75= $329997.38
iv. ?????

Thanks
 
smudge said:
My workings thus far
i.
PV Annuity Due $45000(1-(1.054/0.054)^-19) +1
= $571539.13

Correct!!

ii.
9% *$54000 = $4860
Future Value of Fund = ($60000+$4860) (1.054)^25
=$241541.75

NO.
You can't combine them:
you need to get FV of 60000
then the FV of an ANNUITY of 4860
Click to expand...
 
Thanks for your response.

My workings

ii.
FV= 60000(1.054)^25= 223442.88
PVA= 4860(1.054)^25-1/0.054= 245164.32
223442.88+245164.32=468607.20

iii.
I'm not sure on this question but workings for this are
571539.13-468607.20= 102931.93
102931.93/ (1-(1.054/0.054)^25= 7602.06

iv. ??????/ I'm stuck on this question
 
smudge said:
iv. ??????/ I'm stuck on this question
Click to expand...
iv. If Mary contributes $1,000 for the next 10 years and $3,000 for the remaining 15 years,
will she still meet her target?

1: x = FV of annuity of $1000 (10 years)
2: y = FV of x (15 years)
3: z = FV of annuity of $3000 (15 years)

y + z is what you'll end up with.
 
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