Need help with a calculation

cheerful1_gwMay 14, 2007

If someone invests $10,000 a year for 40 years, leaves all the money intact, assuming a rate of 6%, how much money would that person have after 40 years? What would the formula be?

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My financial calculator had a battery that lasted for years, but gave up the ghost a while ago, and I haven't been ableto find one of the ones that the manual recommends.

You can get one for about $35., and I suggest that it would be a good investment.

Assuming 6% rate of return ... but, firstly ... is that the rate offered by the entity using the money?

If so, do you plan to pay the incometax on the annual earnings from that yer's income, or do you plan to have the invested asset pay it?

If so, and your marginal (i.e. highest) tax rate is 16.66%, you're looking at 5%.

And, do you want to allow for inflation? They say that's about 2% ... but I think they're off of the mark, as I think that it's more like 4%, possibly higher.

If 2%, that leaves you with 3% gain, after allowing for taxes and inflation.

Are you familiar with the rule of 72? That says that if you divide that rate that you're getting into 72, it'll tell you how many years it'll take for your money to double. Dividing your 6% into 72 gives 12, so your $10,000. will double 3.33 times to $33,333. in 40 years.

Taking my figure of 3% (and let's not even think of the possible 1%), it'll double in 24 years, so about 1.66 times to $16,666. in 40 years.

Try it in your regular calculator.

Your $10,000. will earn (whatever rate you choose) for 40 years, and next year that $10,000. will earn that rate for 39 years, then 38 years, etc.

So enter into your regular calculator $10,000. X 1.06 (or 1.03; or 1.01, if you think you'll end up earning about 1%), then press "=", and that figure is $10,600., $10,300. (or possibly $10,100).

The press "M+" to add it to memory.

Then press "=" again, which will show how much the original $10,000. will have grown to, after 2 years, about $11,250.

Then press "M+" again.

If you do not get a gfigure of $10,600. or so after the first "+", reverse the order in which you enter the numbers, until you get thaat figure after the first "=".

The figurethat you entered into memory at first what the amount earned by the $10,000. in one year ... which will be the amount that the $10,000. invested in the 39th year grew to after one year, and pressing "M+" after the second "=" will be the amount that the $10,000. invested in the 38th year grew to, after 2 years.

When you press the "M+" after the 39th time that you press "=", that amount will be the amount that the original $10,000. will have grown to, after those 39 years.

If your calculator runs out of room, use $1,000. as the original figure and multiply by 10.

Good wishes.

ole joyful

    Bookmark   May 15, 2007 at 7:15PM
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Math is not my forte and ole joyful may be on to something. And with luck someone who knows how to input formulas onto an Excel spreadsheet will chime in.

But with a calculator and/or a piece of paper and forgetting about the inflation rates, taxes and whatnot...

10,000 x .06% = 10,600 year one
10,600 x .06% = 11,236 year two
11,236 x .06% = 11,910 year three
11,910 x .06% = 12,624 year four
12,624 x .06% = 13,381 year five etc. etc. etc. 35 more times.

Obviously as your interest earning base increases, it starts to pile up.

    Bookmark   May 16, 2007 at 1:22AM
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    Bookmark   May 16, 2007 at 6:52AM
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Hitting "M+" sounds to me a lot easier.

And - I still recommend getting a financial calculator.

It'll ease a great number of financial calculations, and may encourage you to do more thinking about how money works.

In which case ... I guarantee you that it'll have paid for itself ... hundreds of times over, during your lifetime!

Learning how money works is an interesting hobby - that pays well!

I didn't proofread the earlier post, for I barely made the closing hour at the library, so didn't have time. I was sure glad that I got it finished, though, as I'd have been unhappy to have been cut off, 3/4 of the way through.

Have a great week, what's left of it. Just imagine ... in that day or two, you could learn at least a couple of new and interesting things!

ole joyful

    Bookmark   May 16, 2007 at 7:09PM
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The formula is:

P (1+i)^n Where:

P = Starting principle
i = annual interest rate in decimal, i.e., 6% is 0.06
n = number of years.

the ^ means exponent, i.e., in this case, the quantity in brackecks taken to the "n" power.

You'll need something more than a simple 4-function calculator to do this problem because of the exponent. However, you can construct a table of multipliers with a simple calculator by continuing to multiply by 1.06 for 6% per annum. The mulitplier is 1.06 at the end of the first year, and the multiplier is 1.06 times the previous result at the end of the 2nd year, etc., for example:


The principal doubles every 12 years at 6% interest.
It doubles every 14 years at 5% interest.
However, a more reasonable rate for planning purposes is 4 to 5%.

    Bookmark   May 21, 2007 at 1:31AM
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Are you investing where the current income is taxable?

Then divide the nominal rate of interest/growth by your marginal tax rate and deduct that percentage from the nominal rate.

Are you investing where the number of dollars is guaranteed?

Then the value of each of those invested dollars deteriorates annually by more or less the rate of inflation.

So ... you need to deduct that percentage from the after-tax rate.

That gives you the real rate of return.

Also ... though your expected rate of return now is 6% ... who knows what the institution(s) may offer when you go to renew your contract?

If you invest in assets where you expect the value to increase over the years, you hope that such increase will do as well, and you hope better than, the rate of inflation.

So perhaps you can omit the deduction for an allowance for inflation from your expected rate of return. But ... even so, don't forget that each of those dollars will buy a lot less when you finally choose to use the money.

That is the number that you should use in your calculations.

If not ...

... you're kidding yourself.

I think that it's immoral for me to con others.

I claim that it's just plain stupid for me to con myself.

ole joyful

    Bookmark   May 23, 2007 at 6:02PM
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Here's a simple rule to use on when your money will double. It's called the "rule of 72." Divide your interest rate into 72. The result is how many years it will take for your money to double. So in 40 years, you will have more than $80,000. This is off the subject, but I would not work with 6% interest rates for retirement savings if you are young. I would put that into a Roth and keep adding money as you can. A Roth is tax free to you when you take the money in retirement.

    Bookmark   May 31, 2007 at 12:55PM
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