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How to Calculate Compound Interest?

September 24, 2022
12
min. read

Compound interest is a profit received not only from the invested principal amount, but also from the profit earned as a result of these investments. In other words, once you've made a profit, you put it back into the business and earn interest on that profit too. In this case, the frequency of payouts is important. If you make a profit every day, then you reinvest it every day, which means that the principal amount that’s working for you increases daily, and consequently the profit grows daily. This is much more profitable than if you reinvested once a week, and even more so than if it happened once a year.

How to calculate compound interest? Compound interest can be calculated manually, for example, by compiling a table in Excel. All you need to do is turn on common sense and be attentive. However, once you have done this, you will no longer want to waste time, so the most reasonable thing is to use an online calculator, of which there are plenty on the Internet.

What is compound interest

Let's say you have invested $10,000 and earn 10% annually. This means that at the end of the year you will earn $1,000 and you will have $11,000. In this case, the rate at which your interest was calculated is called APR (Annual Percentage Rate). But what happens if you are offered not an APR of 10%, but an APY of 10% (Annual Percentage Yield) with daily interest payout? This means that you will earn compound interest, and as a result you will receive $11,051.56. We can’t say that the difference is radical, but you have earned more, and that’s a fact. 

Compound interest works well over long periods. With an APR rate of 10% in our example, in five years you will earn $5,000, and with an APY rate of 10% - $6486.08. In 10 years, your principal will double (at APR = 10%), or double and give you an additional $7,179.1 more (with an APY=10%). That is, compound interest will bring in another 70% of the principal amount in addition to what simple interest could bring! 

Anyway, however we juggle numbers around - the benefits are obvious, especially if you add another zero on the right, or imagine that you are saving for retirement all your life using APY, not APR.

Types of compound interest

The more often compound interest is paid out, the more you will earn. This typically happens once a year, once a month or every day. If we imagine that compound interest is paid out not even every second, but every possible moment (i.e., continuously), then we are talking about continuous compounding, which can’t be calculated in Excel, but it is also easy to find a relevant online-calculator.

Periodic compounding

Let's get back to our example and see the results. Thus, when interest is paid out once a year, if you start with $10,000 and a10% APY over 10 years, you will accumulate $25,937. When interest is paid out once a month, you’ll get $27,070. With a daily payout - $27,179. The more often the interest is paid out, the more you will earn.

Continuous compounding

Continuous compounding is a mathematical limit. In this case, you will accumulate $27,183. As you can see, there was no need to worry - the final difference with the daily payout turned out to be about $4. In short, the daily payout is sufficient to avoid the sense that you missed something.

How to calculate compound interest

The easiest way to estimate the compound interest prospects is to use rule 72. It is intended for a compound interest paid annually, but it is suitable for an initial assessment of any option. Rule 72 answers the question of how fast will your principal double? All you need to know is the APY. Divide 72 by APY and get the term.

For instance, APY=4%. 72 divided by 4 is equal to 18 (at this rate, your principal will double in 18 years). Or APY=12%. 72/12=6 (your principal will double in 6 years). If the interest is paid out more often than once a year, then your principal will double a little faster.

The compound interest formula

How to calculate compound interest rate? Formulas are the most boring thing in the world, and you certainly won't have to use them since there are so many compound interest calculators on the Internet. However, let's say miners have used up all the electricity on the planet, and you desperately need to calculate the compound interest right now.  

The general formula of compound interest looks like this:

P (1+i/n)nt

Let's go back to our example and substitute the source data into this formula:

P=$10,000 is the Principal invested

i=10%=0.1 is the Nominal Rate of Interest

n=365 is Compounding Frequency or number of compounding periods in a year

t=10 is the Time, meaning the length of time the interest is applicable, usually expressed in years

Then:

How to calculate daily compound interest? n=365

$10,000 х (1+0.1/365)365 х 10 = $27,179

How to calculate compound interest monthly? n=12

$10,000 х (1+0.1/12)12 х 10 = $27,070

How to calculate compound interest quarterly? n=4

$10,000 х (1+0.1/4)4 х 10 = $26,851

How to calculate semi annual compound interest? n=2

$10,000 х (1+0.1/2)2 х 10 = $26,533

How to calculate annual compound interest? n=1

$10,000 х (1+0.1/1)1 х 10 = $25,937

It works!

Compound interest equation and calculation

Nevertheless, in practice, it is not always possible to calculate compound interest using a formula. The fact is that the interest paid does not have to be constant at all, but may depend on the market situation, the project specifics, etc. For instance, in the Minto mining project, BTCMT hashrate tokens' owners earn mining rewards in Bitcoins daily, but each payout is not equal to the previous one, since it depends on many factors (e.g., the Bitcoin network difficulty or the overall project hashrate may change, and besides, the mining process itself does not guarantee a uniform result). Therefore, even in terms of simple interest (APR), project profitability can only be roughly estimated. 

Minto offers the Autofarming option, which allows you to reinvest daily BTC rewards in hashrate, i.e., to increase your mining power daily and earn even more. However, it is impossible to describe this process with any formula, since payments do not have a strict pattern, except that they occur every day at a set time.

The Excel table comes to the rescue again. For example, here’s a rendering of the results obtained in the first 10 days, while the staking-pool was still almost empty:

Minto profitability in the first 10 days

The right two columns show the amount of daily rewards from 10,000 BTCMT in the case of simple interest (APR) and compound interest (APY when autofarming is enabled). Please note how on the second day, thanks to the reinvestment of the previous day’s $384.3, the subsequent reward payout increased. 

Compound interest traditionally seems more attractive. However, this example is intended to demonstrate that in some cases compound interest cannot be formalized using an equation, but can only be calculated manually.

The benefits of compound interest

Investing in projects where compound interest is paid out on your principal amount is an excellent strategy. You can always earn more, especially if we are talking about significant time periods. If you are choosing between APR and APY, always choose projects with APY. Reinvestment usually occurs once a year, once a month or daily. You can independently estimate the potential profit using rule 72, online compound interest calculators, the relevant formula or the Excel table.

Compound interest is a convenient tool for multiplying profits when all the money is working for you. However, beware of compound interest when it comes to loans and debts. In this case, compound interest can turn against you and force you to pay more than usual.

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