1. ## Retirement Question Finance

The question is:

You want to be able to retire 25 years from now with monthly retirement income of $12000 for 30 years (first withdrawal will be made in 25 years and 1 month from now). You also want to purchase a boat in 15 years at an estimated cost of$60,000. After the 30 year withdrawals, you want to donate $500,000 to charity. You plan to save$2,000 per month for the next 15 years, earn an 8% EAR before retirement and a 6% EAR after retirement. How much will you have to save each month in years 16 through 25?

Not really sure where to start with this one.. Any hints would be much appreciated.

2. ## Re: Retirement Question Finance

Originally Posted by ForeverConfused
The question is:

You want to be able to retire 25 years from now with monthly retirement income of \$12000 for 30 years (first withdrawal will be made in 25 years and 1 month from now). You also want to purchase a boat in 15 years at an estimated cost of \$60,000. After the 30 year withdrawals, you want to donate \$500,000 to charity. You plan to save \$2,000 per month for the next 15 years, earn an 8% EAR before retirement and a 6% EAR after retirement. How much will you have to save each month in years 16 through 25?

Not really sure where to start with this one.. Any hints would be much appreciated.
reposted for clarity.

3. ## Re: Retirement Question Finance

Originally Posted by ForeverConfused
You also want to purchase a boat in 15 years at an estimated cost of \$60,000.
WHEN in the 16th year?
"estimated"??
Provide a date in 15 years (like end of June) and actual boat cost.

4. ## Re: Retirement Question Finance

Originally Posted by DenisB
WHEN in the 16th year?
"estimated"??
Provide a date in 15 years (like end of June) and actual boat cost.
I believe the prof said to assume end of the year unless specified. Anyways, I think I solved it! These are my steps please let me know if it looks right.

First I calculated the Effective periodic rates for before and after his retirement using the given EAR. Then I used the Annuity present value formula to find the PV of the monthly withdrawals and also found the PV of the 500000 he would like to donate. Added those together giving me the sum he needs at retirement to meet his needs.

I then used the annuity future value formula and grew the 2000 he deposits monthly for the next 15 years and then subtracted the cost of the boat at the 15th year.

Next I subtracted the remaining amount after the purchase of the boat from the amount he will need at retirement.

Finally I once again used the Annuity Future Value formula subbing in the amount he still needs as the future value and solved for C giving me a value of about 4413 per month for the amount he must deposit each month.

5. ## Re: Retirement Question Finance

Originally Posted by ForeverConfused
I believe the prof said to assume end of the year unless specified. Anyways, I think I solved it! These are my steps please let me know if it looks right.

First I calculated the Effective periodic rates for before and after his retirement using the given EAR. Then I used the Annuity present value formula to find the PV of the monthly withdrawals and also found the PV of the 500000 he would like to donate. Added those together giving me the sum he needs at retirement to meet his needs. This looks good.

I then used the annuity future value formula and grew the 2000 he deposits monthly for the next 15 years and then subtracted the cost of the boat at the 15th year.

Next I subtracted the remaining amount after the purchase of the boat from the amount he will need at retirement. This is not right because, if I understand you, you are subtracting a present value as of the end of year 15 from a present value as of the end of year 25. Apples and oranges.

Finally I once again used the Annuity Future Value formula subbing in the amount he still needs as the future value and solved for C giving me a value of about 4413 per month for the amount he must deposit each month. This is on the right track, but is vitiated by the error in the previous step.
You are close. Just make sure that you are always dealing with values as of the same date when combining values.

I further suggest when you have your answer that you CHECK it by building a spread sheet. You will find when you try to apply this math in practice that the spread sheets are what convince people. And of course it will let you catch any errors you make before you are embarrassed.

6. ## Re: Retirement Question Finance

Originally Posted by JeffM
You are close. Just make sure that you are always dealing with values as of the same date when combining values.

I further suggest when you have your answer that you CHECK it by building a spread sheet. You will find when you try to apply this math in practice that the spread sheets are what convince people. And of course it will let you catch any errors you make before you are embarrassed.
ah! thanks for that. So I would have to grow the value so it is also at year 25 and then subtract. So in this case it would be growing by 11 years and since it is monthly my t value would equal 132. Just did that and got the correct answer!

11 years?

8. ## Re: Retirement Question Finance

Hmmm...4,413 seems correct to me: 4,413.23 to be exact.

Recap; [montn]:

[180]: 675,213 - 60,000 = 615,213
(4,413 will be next deposit)

[300]: 2,123,128
(-12,000 starts next; interest 6% EAR)

[660]: 500,000

9. ## Re: Retirement Question Finance

Originally Posted by JeffM
11 years?
It would be 11 years going from 15 to 25 no?

Years 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.

Did I misunderstand something??

EDIT: It's till the end of year 25 which is why I am accounting for year 25 as well making it 11

10. ## Re: Retirement Question Finance

I thought you said the boat was bought at the end of year 15. So the accumulation is for years 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, which is 10 years.

11. ## Re: Retirement Question Finance

Originally Posted by ForeverConfused
It would be 11 years going from 15 to 25 no?
How d'heck did you get 4413 then?
4413 is correct IF period used is 10 years.
15 years: deposit of 2,000 monthly
10 years: deposit of 4,413 monthly
30 years: payment of 12,000 monthly
Over and out...

12. ## Re: Retirement Question Finance

Okay here is my working from scratch.

EMR Pre-retirement $= (1+.08)^1^/^1^2 - 1 = 0.64$%
EMR Post Retirement $= (1+.06)^1^/^1^2 - 1 = 0.49$%
PV Of Withdrawals $= 12000[(1 - 1/(1.0049)^(^2^5^)^(^1^2))/.0049)] = 1,890,892.82$
PV Of Donation $= 500000/(1.0049)^(^2^5^)^(^1^2^) = 116,499.32$

Total needed at retirement = $116,499.32 + 1,890,892.82 = 2,007,392.14$

Future value of monthly deposits $= 2000[((1.0064)^(^1^5^)^(^1^2^) - 1)/.0064] = 675,212.60$
This would be the value at year 15 $675,212.60 - 60,000 (cost of boat) = 615,212.60$

Grow the value an additional 10 years so it is also at year 25 $615,212.60(1.0064)^(^1^0^)^(^1^2^) = 132,8174.98$

Subtract value at year 25 from the total needed at retirement $2,007,392.14 - 132,8174.98 = 679,217.16$

Solve for C $679,217.16 = C[((1.0064)^(^1^0^)^(^1^2^) - 1)/.0064]$

I can't seem to find my mistake. I feel like it has to do with the t (year) values

13. ## Re: Retirement Question Finance

Originally Posted by ForeverConfused
Okay here is my working from scratch.

EMR Pre-retirement $= (1+.08)^1^/^1^2 - 1 = 0.64$%
EMR Post Retirement $= (1+.06)^1^/^1^2 - 1 = 0.49$%
PV Of Withdrawals $= 12000[(1 - 1/(1.0049)^(^2^5^)^(^1^2))/.0049)] = 1,890,892.82$
PV Of Donation $= 500000/(1.0049)^(^2^5^)^(^1^2^) = 116,499.32$

Total needed at retirement = $116,499.32 + 1,890,892.82 = 2,007,392.14$
You're using 25 years: should be 30 years.
Total at retirement will be 2,123,126.04

Using .64% and .49% is poor practice:
use at least 4 decimal places: .6434% and .4868%

Exact required monthly deposit will be: 4413.220697....

The remainder of your calculations appear to be ok:
yer smarter than you think

14. ## Re: Retirement Question Finance

Originally Posted by DenisB
You're using 25 years: should be 30 years.
Total at retirement will be 2,123,126.04

Using .64% and .49% is poor practice:
use at least 4 decimal places: .6434% and .4868%

Exact required monthly deposit will be: 4413.220697....

The remainder of your calculations appear to be ok:
yer smarter than you think
Ah! it would be 30 years because the withdrawals are occurring for 30 years not 25 correct? And yeah, I use the full number for the EMR I just wrote .64% and .49% as it's quicker! Thank you all so much for the help