continuous compounding (2023 Update)

At 2 % I would laugh at him. Most of my money is in the stock market and making over 10 % in mutual funds.

.....Until there's a meltdown, that is. A lot of folks are assuming the rigged stockmarket will deliver healthy returns indefinitely. Flawed assumption! But you're both missing the point of the OP's question. Anyone for philosophical calculus? ;-)

If there is a melt-down. Modern governments have gotten pretty good at preventing them.

The stock-market isn't rigged. It is being supported by Keynesian interventions, but this isn't rigigng it - it is preventing investors from panicking and selling their stock much too cheaply. It's not a particularly subtle point, but one that Cursiotr Doom is much too dim to appreciate.

Cursitor Doom is an expert at making them. Less good at identifying them.

Calculus is a mathematical tool, rather than a philosophical one. Compound interest can be compounded as frequently as you like - you just integrate the relevant expression rather than calculating the incremental interest at very closely spaced intervals. It saves a lot of calculation.

He's talking about a problem he got out of some recreational math book, not reality.

Well go on then: answer the OP's question!

Hindsight is 20:20. Tell me what's going to happen next week. Or next month. Or next year. You can't. No one can.

Very wise of him.

Well I hope it works out for you. Personally, I wouldn't sleep at night.

I thought it might be a question he was asked for school.

I still laugh at anything that hardly pays any interist on money that is under 5 % and more like under 10 %. The only thing I even look at is the credit cards I have that give back from 1 to 5 % . While not much, it is money that otherwise I would not get.

There will be a correction sometime. You just have to be prepared for it.

Most likely the compound problem is someones school math problem.

Shortly after Biden got elected I started getting prepared for a meltdown. Moved about 1/3 of the stock into a cash account. That will do two things for me. Still give me some money if the stock goes up. If it goes down I have the cash to take the RMD out of the IRA. If it drops a lot, then I will put the money back in. They say that Buffet is sitting on a lot of cash right now just waiting on a big drop.

I did get out of the market early in the 2000 and 2008 drops and back in as it started back up. Worked out well for me.

That is right. Can't predict the next week or year. However you can look at the trends and if held long enough it will come back stronger if you wait long enough.

I think the market is controlled by a small group and every so often they cause a crash so the small investors will get out at a big loss and the big boys can jump in and clean up. No real facts for this, just what I have in my head.

It's not calculus, it's lim n->oo (1 + APR/n)^n= lim n ((1 + APR/n)^(n/APR))^APR. Given lim n (1+ 1/n)^n=e, see if you can get the answer. Should be a snap for someone who knows everything.

That is calculus, or at least the calculus I got taught. And why bother working it out here? That's what text books are for.

Cursitor Doom doesn't make a point of knowing everything - he just assumes that what he is told by the Daily Mail, Russia Today and Zero Hedge is always correct.

It's just as silly.

I'm not really interested in the calculus you "got" taught since it was obviously a failure. The limiting value is the definition of e, nothing to work out. That's usually what "given" means. What I gave him was a simple exercise in substitution

Oh, but they *are* real facts. The Rothschilds made vast fortunes from manipulating the market in this way going right back to Napoleonic times. If you don't have inside info, you're a small fish in an ocean full of predatory sharks. You need an 'app' that pings you when the likes of Soros, Gates and Buffet all switch to cash. If you haven't got that, you're screwed. If not now, sooner or later.

So... you can't do the sums then.

Not sure about the Mail as I don't read it, but RT and ZH do tend to be proved right more than 50% of the time.

I am 71 and have almost all my money invested in stocks by mutual funds in an IRA. I did move about 1/3 to cash a few months ago after the Election. I do think there will be a big drop sometime evenif it is a year from now. Buffet and some others are said to have a lot in cash now.

I never did get into the bonds market. Just do not want to take the time to study them and how they work. With such a low return on them now, it is just not worth my time.

I have been taking out some of the money to buy things I want in the last few years. The stock has gone up so much in the last few years. I set a number of how much money I wanted to have in the stock market and other cash to live off of. The stock has gone up so much that for my life style I can not spend it( or really not wanting to spend that much). Next year the RMD will be more than I would even think of taking out if the market does not crash, so may just have to put some of that in the stock market . I am playing aorund with about 5 % of the money I have in the market on my own and doing fair with it.

I am lucky that I have a pension and SS to live off of even if I do loose a lot in the market.

As far as the compounding of money goes, I don't really care to get down to the dollar ammount, but just know that the more often it is compounded, the more you make.

Well, at the risk of stating the obvious: you *could* lose all your gains and half your original stake within the next 24 hours. IOW, you haven't made a bean until you crystalize your holdings. Only then will you know for sure how well you've done.

I haven't even given it a moment's thought!

Against whom? If it's me, you have no idea if you did better or not. So I don't dabble in stocks; I'm invested elsewhere and you don't know how well my alternative investments have done. I'm not *that* stupid: I didn't just leave my money in the bank to rot as you seem to imply! :-D

And RichD is still awaiting an exact answer to his question on that very subject from our 'ace mathematician' Bill Sloman!

Instanteous compounding - e^(i*t)

Annual compounding (1 + i)^t

Eg. t = 5 years i = 3% 1.1593 times the original amount with annual compounding

With instantaneous compounding 1.1618

The difference is more significant for higher interest rates..