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Save \$700/mo, Retire In 40 Yrs on \$16k/mo

 by Jim Wang Email   Print

One of the classes I’ve been taking involves investing, discounting cash flows, blah blah; and so one of the things we’ve touched upon is retirement savings. One of our recent problems is calculating how much you need to save in during pre-retirement in order to guarantee (based on assumptions) a future cash flow. So, rather than study the textbook and answer problems with very little payoff (yeah yeah, I have a test), I figured I’d create my own problem and submit it to you all to see if I did it correctly.

Q. How much do I have to save each month for the next forty years in order to ensure that I can withdraw \$5,000 a month, in 2007 dollars, for the next twenty years?

Assumption #1: No taxes. đź™‚
Assumption #2: Inflation will be 3% a year for the next 40 years.

Given that assumption, \$5,000 in purchasing power in 2007 will be \$16,310 in 2047, so you’ll need to have enough retirement assets such that you can withdraw \$16,310 each month (\$195,720 a year) for the next 25 years. In order to calculate that amount, you’ll need to know the rate of return on your assets during those 25 years, as you draw it down.

Assumption #3: Your post-retirement assets will appreciate at 5% a year.

At 5% a year and drawing out \$288,060 a year, you’ll need assets in the amount of \$3,848,183 in Year 40. That means between now and year 40, you’ll need to save and appreciate nearly four million dollars in order to retire on \$5,000 a month (2007 dollars) for the next 25 years. (if that seems a little high, it’s because you have to discount your rate of return by inflation each year) Scary huh?

So, how much do you need to save? Let’s hit up assumption 4…

Assumption #4: Your pre-retirement investments will appreciate at 10%.

Now, in order to have \$3,848,183 in retirement assets in 40 years, how much will you need to save each month if your savings appreciate at 10% each year? (This time we don’t discount for inflation because it’s already taken into account by the payout each month) It’s actually quite reasonable, a mere \$8,694.54 a year… or \$724.55 a month.

17 Responses to “Save \$700/mo, Retire In 40 Yrs on \$16k/mo”

1. Josh says:

Those numbers scare the bejeezus out of me.

2. thomas says:

Is the \$5000 you are projecting you’ll need based on current expenses? Hopefully in those 40 years you will have paid off a mortgage, so if that number was included your savings could drop a little. Also, is this per person? what about your spouse. Do they need to save as much?

I’m saving \$700, but I’m not getting 10% (last I checked).

• jim says:

The other aspects of retirement planning didn’t come into play here, I just chose a round number and ran with it. Your spouse will probably want to save some money and so you’ll have to take that into consideration, it was outside the scope of this particular post.

3. broknowrchlatr says:

I have this exact same calc in my retirement worrkbook so this was easy. I got almost the same number, just 13 cents less at \$724.42. Thats probably due to a difference in when to take the money out during the year, etc.

Now, this supposes you are reall goign to work for 40 more years. Plus, if this is pretax savings in a 401k or IRA, it looks a little more bleak.

40 years is a long time. If you want to retire 5 years earlier than that, you need almost \$450 more savings a month (\$1172.01) and a total of about \$1861.32 if you wnat to retire in 30 years.

• jim says:

I think the 13 cents has to do with rounding, if you’ll notice I rounded everything to the dollar (I think I just truncated it) until the very end.

I’ll build on this and do some comparative number crunching for retiring early, etc. Good to see the numbers were correct though! đź™‚

4. mbhunter says:

No taxes? 10% appreciation? No wonder the amount per month is so low.

These kinds of optimistic assumptions are what get people into trouble and lead them into complacency.

5. avidlurker says:

Any comment from a finaincial standpoint as to the best way to go on this BGE transition ? If there is no intrest accrued, why not opt into the tiered payback system? Any benefit to accepting market rates all at once.

6. Keith says:

Couldn’t you also subtract inflation from your returns and make it easier on yourself? Say 7% returns in retirement – 3% inflation, then do the PV at age 65 to age 90, that’s how much you need in retirement.

Then solve for PMT to age 65 from wherever you are now earning inflation adjusted rates. I think 5% rate (before inflation) in retirement is a little low.

BTW, the TI-83 calculator makes all this very easy for you: 2nd > Finance > TVM Solver, just plug the numbers in.

• jim says:

You actually divide your rate of return by your inflation (1+r)/(1+i) to get the real rate of return (because the two are percentages, it’s a small difference but it’s magnified by the time period).

I’m using a TI BA II Plus calculator but it’s just as easy…

I just chose some round numbers, no real justification for those. 10% may be optimistic, 5% may be pessimistic, 3% may be low for inflation, etc… no one can predict the future. đź™‚

7. jt says:

I put these calculations into an excel spreadsheet a while back (just to play with the numbers pretty quickly and easily). The \$3.85mil looks accurate, although mine shows the ‘nest egg’ nearly playing out after year 24. That might be because I’m calculating based on yearly lump sum disbursements as opposed to monthly. Using that method I show \$159k left in the ‘nest egg’ after year 24 with a \$386k requirement in the 25th year.

One other comment is that while you took inflation into consideration during retirement, it’s not factored in during your working/saving years. If you use the inflation figure and assume you will increase your \$700/month by 3% yearly, then you can attain the \$3.85mil goal by year 37. Put another way, if you adjusted your savings rate yearly by inflation, you could start saving \$533/month today rather than \$700. Put yet another way, if you started with \$700/month today, adjusted for inflation, and worked for another 40 years, your nest egg would be closer to \$5.22 mil instead. Using the same assumptions, that would take you out roughly 37 years into retirement.

8. Sam says:

Where did you get \$288,060 ?? Aren’t you withdrawing \$195k/yr?

Anyway, for monthly payments of 724.55, I get an end result of 4.021 Million in 40 years.

I also got that you need about 3.8 Million if you are adjusting your monthly retirement income for inflation each month.

9. Zook says:

All you can do is save, save, save…

My wife and I put away a minimal \$1100 a month combined, not including monies going to her pension account.

All I can do NOW is make sure this money is properly invested in the proper accounts. I think trying to look into the future [the DEEP, DEEP future like 40-years away] is like talking to one of those silly palm readers. In 2047, things could just be so out of whack and crazy that there is no way to say in 2007 that ‘A’ is needed or that we need to do more of ‘B’.

I think I see these numbers and glaze over real fast.

10. mbhunter says:

Zook, that’s wise. Best strategy is to not get complacent.

11. EMF says:

I follow your explanation for the accumulation phase, coming up with a value similar to your \$3.8M answer assuming contributions are added at the end of the year. But where you make it difficult to follow is the withdrawal part. First you say withdrawals in retirement are \$195720/year, then it’s \$288060. Which is it?

Playing with the numbers and assuming a withdrawal starting at \$195,720 and increasing it by 3% year over year to keep up with inflation, I actually get 26 years, but that’s due to to making the withdrawal at the end of the year. But that’s consistent with having added contributions at the end of the year as well. To get a more precise answer would involve calculating contributions, withdrawals, and interest on a monthly basis instead of a yearly basis. Just a few more rows on your spreadsheet.

But I get the idea. Given that my stated withdrawal approach of adjusting it for inflation agrees with your actual withdrawal approach and not the ones you stated we basically agree on the math. But I have a disagreement with you is on approach. If you’re going to adjust withdrawals for inflation, why not contributions? Yes, I know “power of compounding yada yada”. If you start out with a lower contribution rate of \$535/month and increase that contribution by the inflation rate, then you’ll end up with the same amount at year 40.

That \$189/month difference could be rather important to someone just starting their career. Why should the younger self just starting out scrimp and save so that the relatively affluent older self would only have to contribute the inflation-adjusted equivalent of \$239/month just before retirement?

I recommend a savings approach based on a percentage of salary, not a fixed dollar amount. By doing that, you would automatically compensate for inflation, assuming your salary does as well. Hopefully your salary will increase, but if it does your standard and cost of living will tend to increase, even if you are a saver, so that the equivalent of \$5000/month is not adequate. So a percentage-of-salary approach tends to compensate for changes in standard of living. What the power of compounding means to this approach is that the sooner you start, the lower the percentage of salary saved can be.

And if you want to practice your math, calculate what happens if the inflation rate turns out to be 4% instead of 3%. When you are trying to predict the future, assumption need to be made. But assumptions also need to be rechecked as the actual future unfolds.

Even with an approach based on a percentage of salary, you still need to check where you are periodically and make mid-course corrections. What if your investments make 8% instead of 10%? My retirement planning assumes only that investments keep up with inflation. And if they do better, then I can either adjust my contribution rate or plan on retiring a bit sooner.

12. Chris says:

I used the FV (future value) calculation, and found that:

\$ 3,914,400 would be needed, at a withdrawal rate of 5%/yr, to have \$16,310/month.

And this could be proven, if you presently had \$3,914,400 * 5% = \$195,720/yr, or \$16,310/month.

13. Chris says:

Oh, and to save up \$3,914,400 and assuming an APR of 10%, would depend upon your compounding scheme:
Annually compounding: \$8,760/yr, or \$730/month.
Quarterly compounding: \$7,797/yr, or \$649.75/month.
Monthly compounding: \$7,199/yr, or \$599.91/month.
Weekly compounding: \$7,122/yr, or \$593.50/month.
Daily compounding: \$7,103/yr, or \$591.91/month.

You’ll notice how much faster the daily compounding effect has, even though the APR remains the same.

Caveat that information, in comparison to putting aside \$12,250/yr away at the same APR, with daily compounding for only 5 years, and letting it sit and ferment for 40 years. Your balance will be \$3,718,093.
Which is a longer way of saying, save \$12,250/yr from ages 16-20, earning 10% APR (compounded daily), and serve well garnished when you’re 60 years old.

• MB says:

‘Caveat that information, in comparison to putting aside \$12,250/yr away at the same APR, with daily compounding for only 5 years, and letting it sit and ferment for 40 years. Your balance will be \$3,718,093.
Which is a longer way of saying, save \$12,250/yr from ages 16-20, earning 10% APR (compounded daily), and serve well garnished when youâ€™re 60 years old.’

I know this is an older post…but I just wanted to say: This is sort of what I’m doing. I’m maxing out my 401(k) and Roth IRA for six years (ages 24 – 29). I figure that if I hate mega-corp and/or my life when I turn 30, I can quit. I can do whatever I want to do as long as I can live on the proceeds and not go into debt. And the money should continue to grow over thirty-five years until I turn 65 and can really retire. I call it my “semi-retirement” plan.

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