yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Calculating simple & compound interest | Grade 8 (TX) | Khan Academy


4m read
·Nov 10, 2024

So let's do some examples calculating simple and compound interest.

Let's say we are starting with principal, and I'll use P for principal of $4,000. $4,000. And let's say that we are going to invest it over a time period of four years.

And let's say that we are looking at a rate: we're going to think about whether it's simple or compound. We're looking at a rate of 2.5%. So how much money are we going to make in interest after four years? We're assuming that we are getting 2.5% a year. I want you to pause this video and think about how much money do we have? We earned from the interest in a simple interest situation versus a compound interest situation.

All right, now let's do this together. Let's start with the simple scenario, and it is literally simpler. So here we just have to think about what is 2.5% of 4,000. So we could take 4,000, and then we can multiply that by 2.5%. We could also think about that as 0.025. And then when you multiply it, you could verify this if you like. This is going to be equal to $100.

Now this is how much you're going to get in the simple interest scenario each year. So if you're doing it over four years, you're going to get four times 100, which is equal to $400 in interest.

What you could get another way you could think about it from a simple interest point of view is if I'm getting 2.5% of my original $4,000 per year, well then over four years it's just 4 * 2.5%. I'm going to get 10% of the original $4,000, which once again is $400.

Now let's do the compound interest scenario, and this one is a little bit more involved. Just as a reminder of what's going on with compound interest, we're starting with $4,000. How much will we have after the first year? Well, the first year is going to look pretty similar because it's going to be 4,000 plus 4,000 times 2.5%. So I'll say times 0.025; that's after year one. Let me write this here: after year one would be in that situation.

Now the difference between compound and simple is what we start seeing after year two because then whatever amount that we have here, we're going to multiply that times 2.5% to figure out the new amount of interest that we're getting. Or, put another way, I could simplify this expression up here. I essentially did 4,000 times 1 + let me scroll over a little bit so I don't get too crammed, times 1 + and I will now write 0.025 right over here.

What we're going to do in year two is we're going to take this amount; let me write that down. We have 4,000 * 1 + 0.025 (2.5% right over there). So that's the amount that we had after year one, and we're going to multiply this amount times 1 + 0.025 again.

So it's going to be times 1 + 0.025 again, and so you can imagine if we go all the way to year four, it's going to look like this. It's going to be 4,000, and we're essentially going to be multiplying this thing four times by itself, four times.

So it's going to be times 1 + 0.025 to the fourth power. We're going to be doing this over four years. Now this might look very similar; it might look very familiar, I should say. You might have seen the formula of the total amount over the amount that you're—total amount that you're going to get is going to be your principal times 1 + your rate to the time to however many times you're compounding it to that power.

And so that's exactly what we had here. I didn't want to just directly plug into the formula, which we easily could have done. We could have put the 4,000 here, we could have put the rate right over here, and then we could have put this time right over here to immediately get to this thing right over here. But I wanted you to see where this is coming from.

But let's calculate this, and to be clear, this is going to be the total amount of money we have. It's not going to be the amount that we earned. So once we figure this out, we can then subtract the original 4,000 to figure out how much did we make in interest.

So if we take—let's do this first part—I can add this part in my head, so 1.025 to the 4th power is equal to that. So essentially whatever my principal originally was, I'm going to get this much times that amount is going to be the total amount that I have.

So let me just multiply that times 4,000. So this is going to be the total amount that I have. But now let me subtract the original principal to see how much I have earned in interest. So minus 4,000 is equal to $415.25.

So the amount earned is $415.25. I didn't write it here because this would be 4,400; actually, I could write this here. This is approximately $445.25, but the amount that we earned in interest is this right over here.

And so you can see in this scenario compounding got us a little bit more than an extra $15.

More Articles

View All
a day in the life in Tokyo with my brother vlog
Thank you Sakako for sponsoring this video. [Music] It’s me! Today, I’ve already had my breakfast and I’m currently doing my skincare. We’re going to be getting ready very very quick and then we’ll just leave the house. Today, I’m back with a vlog that …
SCIENCE! What is the Rarest Precious Metal?
Hey, Vsauce. Michael here. And I’m in Anaheim at VidCon. I hope to see some of you here, because I like you guys. But I can’t marry all of you. But if I did put a ring on it, what is the most precious thing you could make that ring out of? Silver, gold, p…
Organism life history and fecundity | Ecology | Khan Academy
We’re going to talk about in this video is what I consider one of the most fascinating subjects in biology, and that’s the variation we see from species to species in life histories and life spans and their rate of reproduction. For example, we have thre…
15 Ways To MAKE PEOPLE TRUST YOU
Hey there. We know how you feel. You have good intentions, but you can’t seem to get anyone to trust you. And worse, you have no idea why anyone would trust you. In fact, this has caused you to trust yourself even less. But did you know that all of that c…
A Mexican Wolf Pup’s Journey into the Wild | Podcast | Overheard at National Geographic
Foreign [Music] This is what it sounds like to explore New Mexico’s Gila Wilderness on horseback. On a recent assignment for National Geographic, I got to venture deep into the Gila with a photographer, podcast producer, and a backcountry guide. The Gila …
Comparing P-values to different significance levels | AP Statistics | Khan Academy
What we’re going to do in this video is talk about significance levels, which are denoted by the Greek letter alpha. We’re going to talk about two things: the different conclusions you might make based on the different significance levels that you might …