Compound Interest Explained
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- Опубликовано: 28 авг 2024
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Compound Interest is the concept of "earning interest on interest." Albert Einstein called it the "8th Wonder of the World".
Essentially, the difference between simple interest and compound interest is whether or not earned interest is capitalized, or reinvested, and added to the original investment amount.
Simple interest is not added to the original principal, So the amount of interest earned each period does not change throughout the life of the investment.
Each time we earn interest, those earnings are added to the principal. So in future periods, we are earning interest not only on our principal, but we earn interest on our interest, too. And that is the fundamental concept of compounding interest, is that we earn interest on interest.
COMPOUNDING INTERVALS
Important to note is that we always express interest in what we call "nominal" terms, which is, we express interest in its annual interest rate. - 12% "per year".
We don't always earn interest just once per year. So we might have a nominal rate of 12%, but we could have compounding just at one time at the end of each year, we could have in interest paid evenly every month so in the case of the 12% interest rate we would make 1% of interest per month, or even daily. There are really are no limits to how you can slice and dice that, except that the interest should be paid in regular intervals.
Now of course, in the real estate world, and the vast majority of investments, we see monthly compounding, and going forward, we will primarily focus on compounding interest with monthly intervals; however, for this example, I want to show you how it works in each way.
So if we have monthly compounding, and instead of getting paid interest once per year, we're getting 1/12 of our interest every month, that means throughout the year we are earning more interest along the way and the curve is a little bit steeper. In the case of monthly compounding, at the end of the first year we would have $1127 instead of $1120 because we're getting paid interest more often, and therefore earning interest on our interest earlier and more often.
At the end of the second year, we would have $1270, and at the end of the third year we would have $1431.
If we had all the interest up that we earned over that year, we would have earned $431. So you can see, with monthly compounding, we get a little bit more interest on our interest than we do with annual.
Monthly compounding we would earn $4307, and with annual compounding we would earn $4049.
So, as you can see, the more frequently you compound your interest, the more you earn.
The effect of varying compounding intervals is what creates the difference between the 'Nominal Rate' and the 'Effective Rate', also known as the difference between the APR and the APY.
APR stands for "Annual Percentage Rate." That's nominal rate that is quoted.
But as you can see all of these earn 12%, but
based on the compounding, they have different yields. That is the "Annual Percentage Yield".
If we go back and we look at the true yield, or true
interest rate earned, also known as the "effective annual rate", we will see that the more often we compound, the higher the effective yield goes.
When you have annual compounding
your interest rate is always equal to the nominal rate. Your effective yield or annual percentage yield is the nominal rate because interest is being paid once per year.
But doing the math on the other two we'll see $431 being a 12.6% annual yield, and with daily compounding it's 12.75%. So note how our quoted rate is 12% but the effective rate is 3/4 of a point higher.
Now the same applies in a loan, so if you have, say, a 12% interest rate quoted on a loan on which you are the borrower and it's monthly compounding, your actual effective rate is 12.6%.
It's usually compound interest, and certainly in real estate, almost everything, including mortgage loans and rents, are usually done on a monthly basis. And so real estate loans typically use monthly compounding.
The "nominal rate", or the named rate, also known as the APR is typically different than the "effective annual rate" or the Annual Percentage Yield.
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QOTD: What lessons or concepts would you like me to teach you? Tell me below! - Trevor
Thank you sir, your video was very informative?
You’re very welcome!
I'm having a hard time understanding how you got $127 for the first year on monthly compound interest. Could you give a formula example please?
You can learn how to do that in my free course here: learn.realestatefinanceacademy.com/finance-prerequisite
Hope that helps! - Trevor
Thanks Trevor
Very welcome. Happy to help! - Trevor