 So, on page 197, this lesson actually comes before the exponential growth lesson. I flip-flop Holly from year to year when I first taught this. I taught this first and then I taught the generic exponential growth and then I thought, you know what, it's probably easier to teach them the generic one and then show them how this fits into the generic one because there's two ways to teach compound interest. One is to memorize another equation and I'm not big on memorizing yet more stuff. The other way is to memorize A equals A0 times C, the T over P, that generic exponential growth equation and just tweak it to fit compound interest. But first I'll talk about what compound interest is. Every one of you almost certainly will borrow money sometime in your life. Probably for a house, possibly for a car, maybe for that shiny new boat or whatever. Why do banks lend money? The answer is they make money when they lend you money. How do they make money when they lend you money? They don't lend you money for free, they charge you a fee. What do we call that fee? Interest. They charge you a percentage except the banks are very clever, they want to make more money. Holly, they charge you what's called compound interest. What that means is they charge you interest on the interest and then next time they charge you interest on the interest on the interest. If you ever take out a big loan, like for 10 years, you'll be amazed when they schedule your payments to find that your $10,000 loan ends up costing you $18,000 and you actually only pay off that $10,000 in the final three years of your 10-year set. The first seven years are doing nothing but paying off the interest on the interest on the interest on the interest. The reason, Amanda, is what does every single exponential growth graph look like? Okay. Yeah. Financially, the longer you have that loan, the faster that interest grows and so paying that off is the tricky part. If you get an investment that compounds, that's a good thing. This is why we tell you if you're young to try and put some money into a term deposit and by the time you're 50, it'll probably be $1 million, starting out with a couple of thousand, as long as you don't touch it. In simple interest, the principle at the beginning of the second year is the same as the principle at the beginning of the first year. What the heck is the principle? That's how much you borrowed or invested your starting amount. In simple interest, the starting amount doesn't change. That's not how the real world works. In compound interest, the interest earned or charged in the first year is added to your principle. Now in the second year, you owe more money and they're going to charge you interest on the more money. Turn to page 198, blah, blah, blah, blah, blah, blah. Turn to page 199, blah, blah, blah, blah, blah, blah, blah. What I really want you to do is turn to page 200. I think it's easier for me to just jump straight into an example. It says here, compound interest formula. There is one. It's this thing. What I'm going to do is I'm going to put one line through this and I'm going to write A equals A0C to the T over P. Does that look familiar, Carson? We're going to try, instead of memorizing yet another equation, we're going to see if we can't tweak it to fit this. Some of this we already know, A is the final amount, P, which I'm going to call A0. That represents the initial amount. C is going to be one plus the interest rate. So I'm going to put the little i right there. I represents the interest rate per compound period because we're increasing by a percentage. We're going to go one plus that amount, cross out the N. T is total time and P is the length of a compounding period. Sounds confusing. It's not. In fact, it's much easier to just do an example. So once you've written that down, let's scroll down to example one. Now they've given us letters to fill in. We're going to ignore those letters to fill in somewhat. So I'm going to go $7,000, I think that's my initial amount, is invested in a six year GIC. What's a GIC? Something, something, I can't remember what it stands for, an investment compounded quarterly at a rate of 5% per annum. Determine the value of the investment at the end of the term. I'd like you to do a couple of things. Can you underline the words compounded quarterly? And can you write our template A equals A0C to the T over P? What are they asking you to find in this question? Can you interpret that? Are they asking you to find that, that, that, that, or that final amount? So I'm going to go like this, A equals question mark, and now I feel better. What's this? What's my initial amount, $7,000? What's T, six years? What did I underline? That tells you the length of one period. P is a quarter of a year. Tyson, what if they had said compounded monthly, what would P be? I caught you zoning out, didn't I? Okay, where did that P equals one quarter come from? Compounded what? Quarterly. So what if it was compounded monthly, what would P be? 112? Here's all the possible phrases. It can be monthly, quarterly, it can be semi-annually, P would be what then? A half? It can be yearly, P would be one. Weekly, P would be 52, one over 52. Daily, P would be one over 365. Shut up, bags, don't do that. A lot of them will do compounded infinitely and use base E because that's a continuous growth model, yeah, because they want to make as much money as they can. Getting dramatically new there, here is where we have to make a little adjustment. Once you've written C equals, put your pencils down for a second. What's my growth rate here? At first glance, you might say, oh, 5%, don't write this down. You might be tempted to go 1.05 because remember Kirsten, it was 1 plus the percentage if you were increasing or 1 minus the percentage if you were decreasing and you've made a very, very, very subtle error and this is the only tweak that we're going to have to do. It's still going to be 1 plus. Steph, can you read that to me? What does anam mean? It's a financial term. It means per year, but what's my growth period? A quarter, you ready? Look up. If the interest rate is 5% for a whole year, what's the interest rate for one growth period for a quarter of a year? What am I going to have to do with that interest rate that they gave me in years so that I can fit it so that it matches the units of my compounding growth period? Take that 5% and divide it by what? 4. That's the adjustment we're going to have to make because our interest rate and our period have to be for the same length. It's going to be this, .05 over 4. That's what you can write down. Tyson, what if it was monthly? What would I divide that 5% by? What if it was daily? What would I divide that 5% by? 365. What if it was semi-annually? What would I divide that 2? That's the tweak, Shannon, that we're going to have to do. This is going to give us final amount equals initial amount 1 plus .05. .05 over 4, close bracket, to the power of 6 divided by 1 quarter. Is that okay so far? Amanda, how do I divide by a fraction? Well, multiplying by a fraction, that was the easiest one. It was top times top, bottom times bottom. Dividing almost as easy is multiplied by the reciprocal. In fact, this here is really the same as 6 times 4 over 1. In fact, dividing by a quarter is the same as multiplying by what? More specific. Dividing by a quarter is the same as multiplying by what? 4. Yes? Dividing by a half is the same as multiplying by what? Dividing by 1-12 is the same as multiplying by what? That's why, even though I scribbled it out in the original formula, N is the number of compounding periods, 6 years, 4 times a year, 24 times, 6 years, 12 times a year, 72 times. You know what? I can memorize a whole new formula, or I can say, I can divide by a fraction without killing myself. Anyways, that exponent there is really going to be a 24. Andrew, what am I trying to find? Is that an exponent? Logs? No. Is the a by itself already? Well, heck, this is straight calculator then. I'll be careful in my typing, but it's going to be 7,000 times bracket 1 plus 0.05 divided by 4 close bracket to the power of, and I could go 6 divided by 1 quarter, but I know what is 6 divided by 1 quarter. I'm just going to type a 24 there. After 6 years, what's this investment worth? We're talking about money, so I shouldn't need to tell you what to round off to. What do we always round off to when it comes to money unless they say different? How many decimal places? Dollars and cents, right? So I'm not going to say to you if it's a money question. Round off to 4 decimal. I'm going to assume you clue in. This ends up being 943 1.46, 943 1.46. That's the value. How much did he earn? Well, how much did he start out with? Or sheet? 7,000, I guess they earned $2,431.46 on their return, or if it was a loan, you would end up paying an extra $2,431.46, because you're too impatient to save your money, or in the case of a house, you just couldn't save that much money, you had to pay it off over your lifetime. Probably I'll be more interested in trying to find those numbers because they're exponents and logs, but let's see. Example 2, we're going to come back to. Example 3, Barbara invests $8,000 in an account which pays compound interest of 6% per annum. I'm going to underline the phrase compounded monthly. How long would it take to the nearest necessary month for her investment to double in value? Okay, I'm going to scribble out these. I'm going to write down A equals A0C to the T over P. Do I know that? 8,000? Do I know that? 16,000? I agree with Carson, but I also disagree with Carson. Did they say they want the money to double in value? As my shortcut, I could also have simply said, let my initial amount be 1 and my final amount be 2, because when I divide that 8,000 over and put it underneath the 16,000, you know what? 16,000 over 8,000 is going to end up being 2. I don't care what you do, but I'm lazy. I'm going to put a 2 and a 1 there just because I can. XC, well, that's going to be 1 plus 0.06 over, what are the compounding terms of this one? What did I underline? What am I going to divide that puppy by? 12. Usually, I check if it works out evenly, nicely on my calculator, 1 plus 0.06 divided by 12. You know what? I'm going to write 1.005 from now on, because that's easier to write. If it worked out to a yucky, long, repeating decimal, then I'd probably actually just keep writing this in brackets. Is that okay, Katie? 1.005. What are they asking me to find in this question? I don't know. Okay. Do I know the growth period? What? No? Think carefully. Do I know the growth period? Amanda? What? 1.12 compounded monthly. By the way, Amanda, dividing by 1.12, same as multiplying by what? More specific. Dividing by 1.12, yeah, okay. When I give you the number, I'm looking for the answer. Dividing by a fraction, same as multiplying by what? The reciprocal. Dividing by 1.12, same as multiplying by 12. I think they're asking me to find t, which is an exponent, which means, woo-hoo, logs. I think I'll have this, 2 equals 1.005 to the power of Amanda, look up, yes? Dividing by 1.12, same as multiplying by 12, and that looks less terrifying to you guys, because you guys seem to hate fractions. I like them. Me and fractions, BFF, in fact, BFFF, best friends forever fractions. Is that okay, Sabrina? Where's the variable sitting? You know what I'm going to end up doing? Log of both sides. Now, if I'd written the 8,000 there and the 16,000, I would, first of all, divide it over to make it easier. We were clever. Is that one going to make a difference? Then I say, and we're going to take the log of both sides right now. We're going to get this. The log of 2 equals the log of 1.005, and that 12t is going to drop to the front there, isn't it? I did that on one line because I'm running out of room. How would I get the t by itself? How would I get the t by itself? More specific, but yeah, whoever said divide, what am I going to do with this 12? Divide? What am I going to do with this log? Divide. You know what? I think t is going to end up being the log of 2 all divided by 12 log of 1.005. I typed something in wrong. What did I type in wrong? I can't believe I did it. If I'd done it on purpose, that would have been great teaching it. How many numbers on the bottom? How many terms on the bottom? Two? Did I use brackets? No. Close off the log, close off the bottom. Ah, that looks better, 11.58 years. This answer doesn't want an answer in years. What does this answer want its answer in? Months. Okay. How do I go from years to months? Divide by 12? So you're saying 3 years is 3 divided by 12 a quarter of a month? Ah, what? By the way, did I just give you a fairly easy way to figure it out yourself, right? Times by 12. And since I have this number here, times 12, 100, and oh, it says to the nearest necessary month, 139 months. Try number one, try number three, and I think you can try eight. And then I also have for you today two take home quizzes. Let me hand those out. Two? Yeah, sorry. It's the way it's going to work. It's coming up.