Discrete Compounding

Categories: Metrics, Investing, Bonds, Stocks

Financiers aren't that different from chefs. They have to decide how much of what to put where, find the best method of mixing it all together, and keep customers coming back. They are artisans of their crafts.

In finance, “discrete compounding” is a recipe that has multiple variations. Discrete compounding is a method of calculating compound interest at certain points in time. Compounding interest, as opposed to simple interest, is where the interested is calculated, then added to the principal before the next round of interest is calculated. Because the new interest at each calculation round is added to the principal, a loan with compounding interest will rise much faster than a loan with simple interest (think: exponentially rather than linearly).

The “discrete” in “discrete compounding” just means this snowball process happens at certain intervals of time, say weekly, monthly, or possibly annually. This is different from continuous compounding, which, as the creative name would have you assume, is compounding continuously (usually daily, but it could be more often), and not at set intervals of time.

Let’s think about your bank account and how it calculates interest that it gives you. You might think having an account that has more instances of compounding would mean much more money for you, but it doesn’t. The more often the money sitting in your bank is compounded, yes, the more money you will get technically, but by a lot less than you’d think (like...a lot less).

For instance, one round of compounding (i.e. an account with annual discrete compounding) on $1,000 at 2% would get you $1,020. If your account was continuously compounding (daily) for a year on that same $1,000, then you’d have $1,020.20. Yep, compounding that $1,000 365 times in a year only gets you 20 cents more than compounding once in a year. Still, because compounding interest grows at an increasing rate, that can add up over time, bit by bit. By bit by bit.

By bit.

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Finance: What is Compounding Value or Co...1773 Views

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Finance allah shmoop What is calm Pounding value or compounding

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interest Ah the power of compounding it makes tree's stronger

00:12

pollution More feral and the rich Well richer How so

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Well let's start with compounds kissing cousin with six toes

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Arithmetic calm pounding Right So the first was really geometric

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compounding Now we're talking about arithmetic compounding If you invest

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a thousand bucks in a ten year bond that pay

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six percent a year in interest the dough comes back

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to you in a pattern that looks like this Like

00:35

every six months they pay thirty bucks and it's sixty

00:38

dollars a year Got it nice You get the total

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of sixteen hundred bucks back from your investment And the

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cash that came back to you you know came in

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small parts all along the way until you got about

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two thirds of it or sixty percent at the end

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right If you just spent that money and collected your

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thousand bucks at the end That's it Okay So that's

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arithmetic compounding the money comes to you You don't reinvest

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it Ding ding ding that's the key here and you

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just go buy burgers Okay So now let's look at

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what six percent compound id looks like over the same

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ten year period Wealth at the end of your one

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it's a thousand sixty bucks and no we're only going

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to compound it annually We probably should do the semi

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annually but we confuse you even more is we won't

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do that but then you essentially re invest that money

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and you get another six percent compounded on that thousand

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sixty instead of six percent compounded against the original thousand

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so by the end of your two you'll have a

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thousand one hundred twenty three sixty and by the end

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of your ten you'll have one thousand seven hundred ninety

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dollars and eighty five cents So why do you make

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so much more money when you compound interest versus getting

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thirty bucks twice a year like you would in this

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bond example going by and burgers with it You don't

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wanna do that well essentially what's happening is that you're

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delaying your gratification of getting that sweet sweet cash or

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getting liquid Whatever you wanna call it by reinvesting your

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gains year after year after year So do you have

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that sort of self control Do you need the cash

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Yeah that's The question If you for example have trouble

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making it home from your local pizza spot with the

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pie intact well and compound interest Keeping the discipline to

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not spend the money today and wait for the happiness

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tomorrow Well when that may not be for you Sorry

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