# Loan amortization – TBS open teaching

Have you ever been laying in bed late at night and asked yourself I wonder how loan amortization works? I have, I do it all the time and I’m a great guy! Today I will show you how loans are amortized, in other words, repaid Fancy word isn’t it? So imagine a bank offers to lend you $5,000 on simple terms: for 5 years, you will make equal payments at the end of each year and the annual interest rate is 20% How much is this loan going to cost you? To answer this, you need to figure out the size of each payment Let’s first look at the $5,000, which we call the principal amount. Now, you might think, five thousand dollars divided into five payments, that’s one thousand dollars per payment Well that’s a very simplistic way of looking at it, ok. The problem is, $1,000 payments will not be enough to repay the loan in five years so the bank will not agree to it Cause they’re not stupid Before understanding this, you have to remember that repayment of a loan must be such that 1) you pay interest each period on the current remaining loan balance 2) you reimburse part of the principal Easy, easy two rules, right? So in this case, after one year 20% interest on your $5,000 loan amounts to $1,000 so when you pay $1,000 at the end of the year, it’s just enough to cover the interest, and thus there is not enough money to also start to repay the amount you owe That’s why by the end of the year you still owe the bank $5,000 Oh, this isn’t working… The same thing happens the second year and the third and the fourth and even after the fifth year you still owe the bank $5,000 What’s going on? Why is this not working? So, if you keep going on this way, the loan is never going to get repaid, ever Now, what if you double your repayment to $2,000 per year? Because you’re a big spender Because you’re a big spender Then after one year, your interest will be $1,000 but you will make a payment of $2,000 so that’s enough to not only cover the $1,000 interest payment but also to reduce the total amount you owe, by $1,000 So that’s your first principal repayment So by the end of the first year you will owe the bank only $4,000 That’s progress, isn’t it? Then the following year, your 20% interest is $800 but you repay $2,000 again again because you’re a big spender which is enough to pay the $800 and repay $1,200 of the remaining balance so by the end of the year, you have a balance of $2,800 This is getting pretty good, isn’t it? Looks like you’re paying it back In year three, your interest is 20% of $2,800 or just $560 so your principal repayment is $2,000 less $560, or $1,440 which brings your loan balance down to $2,800-$1,440 or $1,360 which happens to be my favorite number! If you continue for one more year the same way you will see that you will be paying the bank too much by the end of the year you will have a negative loan balance! And that is not good I mean, for you it’s not good, for the bank it’s amazing. So for a $5,000 loan with 5 payments and a 20% interest, paying $2,000 is too much and $1,000 is not enough So what is the right amount? You could try, for example, $1,500, and keep trying until the amount is just enough so that by the end of the fifth year, you don’t owe money to the bank, and you haven’t overpaid But instead of doing all the hard work yourself, you can ask the computer to do if for you I know, why didn’t I just tell you that at the beginning? Because I want you to learn the basics first. In Excel, just type in this … I’ll translate this to English. It means: “Calculate for me the payment amount if the interest rate is 20%, I have 5 payments, and I borrow 5,000” You will immediately have the answer: 1,671.90 which happens to be my fourth favorite number You thought it was going to be the third, didn’t you? No, I’m not going to tell you that one, that’s my secret number That’s exactly how the bank will calculate the number for you Does this payment work? Let’s check after one year, you owe the bank $4,328.10 After two years you will only owe the bank $3,521.83 And after three more years, you will be done Thank God Let’s see the full table I hope that TBS video production people will put up a nice table on the screen like they promised… just like the bank hopes that you’ll make your payments like you promised sometimes promises are never kept… Aha, sorry for losing faith, here is the table It’s called a loan amortization schedule because it shows how your loan is getting amortized, or repaid, over time Fun fact: “amortized” comes for the Latin root of being killed off; so it’s fun watching your loan being killed off. When a bank offers you a loan, it has to show you what the amortization schedule looks like so you can literally watch your loan die. As you look at the table, note a few things. The first column shows you the years The second column shows you how the amount you owe at the start of the year initially equal to the borrowed amount of $5,000, is becoming smaller and smaller Just like my dignity So the interest on the loan, shown in the third column, which is equal to the second column times the interest rate of 20% is also becoming smaller and smaller The payment amount in the fourth column, though, is staying constant just like the noise my neighbors make at night that’s because most loans have fixed payments just like my neighbors have fixed habits And as the loan matures, since there will be less and less interest to repay we can see in the fifth column that each payment serves to repay more and more of the principal And as a result, the ending balance each year is becoming smaller and smaller until at the end of the fifth year, there is nothing left to repay So, how much would this loan cost you? Well, you’ve just looked into the future and saw that you would end up making 5 payments of $1,671.90 so you altogether would spend $8,359.50 Oh my God that’s my third favorite number… I didn’t want you guys to know but I guess now you know This means you would pay an additional $3,359.50 in order to borrow five grand Is that good or is that bad? This depends on what other banks are offering, on what you can afford to pay and on how much you need the money We could talk about this for hours, but I think we’ve learned enough on loan amortization [Offscreen voice: What about the time value of money?] Thanks for tuning in, we’ll catch you next time! So I think it’s about time we (w)rap this up: this is Sammy Obeid,

I’ve shown you how debt is repaid, ’cause knowing loan amortization

can save you moans and aggravation And just know I did not write that Thank you so much for tuning in, catch you next time.