I am trying to get my math in order, been a while since I’ve done this kind without a calculator and I want to be good enough to handle my own taxes (no H&R block). So here’s the question. What is the best way to figure compound interest on something, no calculator involved? If possible, in the best laymans terms. An example: How the hell do I calculate let’s say how much the Interest on a million bucks (1,200,000) dollars if it was compounded monthly for 10 years at 5.7%. How would I figure out how much of the 1,200,000 came from interest? and what about the rest?
Thanks, this can be very helpful, if only I was sitting on 1,200,000 it would be more helpful.
Well, nothing to do with taxes to be honest, I just figure if I set the bar really high in doing computations like this, I will be knowledgeable enough to handle taxes and maybe calculating the worth of an IRA and such before I get one… sadly I don’t have one yet, 28, still in school, and have a job(s) that pays well, but not enough.
None of the calculations in doing taxes are complicated. It’s all just grade-school stuff, mostly just addition and subtraction. There are just a lot of them, and figuring out which of the calculations to do can be complicated.
And here’s the reasoning behind the formula, in case you care:
Let’s say the annual interest rate is 6% (r = .06), but it’s compounded monthly (n = 12 times a year). Then each time the interest is compounded, r/n (in the example, .06/12 = .005, or 0.5%) of what you had before gets added on.
So, if you start with P dollars, after the first compounding you’ll have P + P*(r/n) dollars. You can factor out the P and write this as P(1 + r/n). So your original amount got multiplied by (1 + r/n).
After the second compounding, the amount you have after the first compounding gets multiplied by (1 + r/n) again, so you now have P(1 + r/n)(1 + r/n), or P(1 + r/n)[sup]2[/sup]. After the third compounding, you have P(1 + r/n)[sup]3[/sup]; and so on.
If you compound n times per year, for t years, that’s nt compoundings in all, so the amount you end up with at the end of that time is P (1 + r/n)[sup]nt[/sup].
Maybe I’m not following you, but it seems like you might be referring to the fact that the IRS mandates use of their tax tables with pre-calculated taxes based on filing status/taxable income.
But those tables only go up to $100,000 of taxable income - after that you have to calculate it yourself.
Also, the filer generally calculates the difference between taxes withheld throughout the year and the actual tax owed at the end of the year which determines whether an additional payment to the IRS is required or a refund due.
Maybe you were referring to the option to have the IRS calculate total tax owed and the balance to be paid or refunded? But there are a lot of circumstances in which they cannot do so, including something as common as itemizing deductions. See page 208 of Pub. 17.
Historical note: Interest calculations were done even in ancient Sumeria. While compound interest calculations often were very crude, a [del]cuneiform[/del] PDF text from before the time of Hammurabi derives, correctly, that a loan with 20% interest will double in slightly less than 4 years.
When you say “without a calculator”, do you mean without a specialized compound interest calculator or without an electronic computing device of any kind?
Generally, interest is taxable as ordinary income … and you will need to report it … interest on IRA’s and the like are treated differently and I’m not sure how that all works …
The good news is that any interest you earn will be reported to you on an IRS Form 1099-INT … simply look for the space that states the taxable interest and enter that onto your 1040 spp …
Way way way back in the Not-Quite-as-Dark-as-the-Dark-Ages … even before PDF … even before electronic calculators … we had these things we called “books” … and certain “books” were just tables of interest values … many many “books” that covered just about any loan period, interest rate, and initial values … really exotic stuff, maybe ask your grandparents about it and perhaps they might have some of these “books” up in their attic or someplace …
Just amazing what was done during the Proto-Silicon Era …
That is exactly the reason why I want to know this stuff, just so I can always be prepared to figure it out. Also, yeah I meant without a calculator of any kind, I know the thought is dreadful, especially to myself even though I consider math to be demonic lol. Duckster Yeah, seems like by the end of this year I’ll be shopping around for one and start with some good low risk investments. Speaking of which, any tips?
Since you are just starting out and have a long investment period, I suggest you go to The Dough Roller and listen to podcast DR 178. It talks about fees and the effect they have on your investment growth.