TI-84 Calculator – 36 – Calculating Mortgages and Loans

hello and welcome to the section of the tutorial where we’re going to continue looking at financial calculations with the ti calculators and in this this chapter we’re going to specifically look at what we call the time value of money we all know that as we take out loans for various things you know we’re paying more than the cost of the item that’s just out how the world works so when you when you buy a house let’s say your house cost a hundred thousand dollars you know and you take out a loan for thirty years you’re going to pay a whole lot more than a hundred thousand dollars for that house of course the advantage to you is that you’re doing it over 30 years that you can afford to make those payments whereas most people don’t have a hundred thousand dollars laying around to pay cash for a house so the time value of money calculator here in the TI calculator lets you quickly quickly quickly do these calculations and we can do a lot of great things with it and really learn how different loan terms could really help you or hurt you so in order to take a look at it let’s go in the apps menu under finance the very first thing is TVM solver time value of money and I think this is eye-opening for most people until you sit down and start playing around with loan numbers you know you really it’s hard to imagine how much money people pay for houses and cars when we take out long loan so let’s take a look at it what we have in here is a bunch of variables I’m going to explain what they all are they’re very easy to understand but the basic idea is you fill out what you know and then the thing that you don’t know you put the cursor on that line and then you hit the solve button and then the calculator is going to try to solve for the variable that you that you have the cursor currently on so as a as an example let’s say you’re going to buy a house and you’re going to take out a 30-year mortgage so 30 years times 12 months is 360 months so you’re gonna pay 360 payments and that’s what n is equal to and actually I should have told you I’ll do this now before we jump into here too far let me go out of here and go to the mode menu when you’re dealing with money it’s a very good idea to get the float on two decimal places and that way everything’s gonna look like a nice dollar signs coming out of there so we’ll go back to the apps menu back to the finance menu and notice that our our 360 is still there but everything has two decimal places so this is how many payments you have if you had a five year car note it would be 60 payments so you put 60 here so whatever the term is that you have however many checks you’re gonna write over the entire life of the loan that’s the number you put in there this number is the percentage rate interest so for this particular example let’s choose 8 percent interest on a home this this number here is this PV stands for present value and basically that’s the value of the home that you’re buying or if you’re buying a car it’s the value of the car so for now let’s just put something 250 thousand dollars you know you can put any number there this is for a car then maybe your your car is gonna be you know seven thousand dollars that you put in there all right monthly payment that’s what I’m gonna actually calculate first so we’re not gonna put anything there FV is future value I’ll tell you about that later don’t worry about that right now it’s pretty easy to understand but it makes more sense after we do the calculation the next one is P /y it means payments per year so it’s just asking you because the calculator has no idea what you’re buying you have to tell it okay you told it you’re making 360 payments on the life of the loan but you need to tell it how many payments in one year most people pay monthly so this is going to be 12 this is going to be 12 now just below it there’s a line that’s C /y this means compounding periods per year so most of the time if you’re making 12 payments your loan is going to be compounded monthly as well so it’s going to the calculator notice automatically put a 12 there I didn’t even do that that’s an automatic thing you can override that if you need to but that’s that’s the basic idea so I think now we’re pretty good to go this this tells you if you’re making your payment at the end of the month or the beginning of the month and you can change that as you need but for the purpose of teaching it’s not not important so you put what you know in a number of payments interest rate value of the home and how many payments per year and then if you want to calculate the payment this is this is what your monthly payments going to be like if you’re actually at a car dealer ship trying to figure out what’s my monthly payment gonna be you could whip this sucker out and figure it out right away the way you figure this out you make sure the cursor is on this line then you hit alpha and the reason you’re hit alpha is because you have to hit the solve button right here and then notice that it pops out with a number there’s a little square next to this which means the calculator has calculated the answer there as opposed to these other fields that don’t have a square that’s because you input these numbers yourself the calculator calculated this one and your payment is negative eighteen thirty four dollars and forty-one cents per month the reason it’s negative is because this represents money leaving your wallet so it’s cashflow leaving you so it’s why it’s negative all right so this is your monthly payment so you can play around with this you could say well for a $250,000 house this is gonna be my payment well what if my interest rate drops to 6% what does that do so I have to enter the new interest rate and then I go up to here to payment again alpha Sall and instead of 1834 it’s 1498 so you get you have less payment per month if you can get a little bit less interest rate you can certainly pay less per month which is what most people are trying to do now another thing is the future value this is what FV means so you’re making these payments almost $1,500 a month and you’re doing it for 360 months so if you go here and you calculate future value this is going to calculate what is the future the future value of basically of my loan here if I pay these payments out for 360 months if I hit solve on this line it’s going to stay 0 but what if I go up here and I say what about after only 10 months of pain what if I put a 10 in here then if I go down here to future value because this this number here this 1498 this is now fixed this is this is in the calculator as a variable if I go to future value and solve now this number is going to be two hundred and forty-seven thousand four hundred and fifty four dollars so what this means when you go and solve for future value is if I start a loan for $250,000 its 6% interest and I’m making a monthly payment of this then after 10 months I have paid down that loan so that the balance is basically this much money two hundred forty-seven thousand four hundred fifty four dollars that’s basically what it is so you can also use this in the in the positive sense if you’re putting money in a CD or something you could put the present value in there you could put positive interest rate and then you could you would basically count you would be calculating in that instance what the bank is paying you and you would also have a positive future future that value here because your money would be growing but in this case you know your money your money isn’t so that’s what that’s doing right there now one more thing I want to tell you is that the calculator once you make these calculations let’s say you calculate them to monthly payment but you want to use that in another calculation like on the stack here you want to multiply it by five or something like that so instead of typing the number in again you can just go back to the finance menu and go down and you see right here TVM payment TV and % TV M present value future value and so on if you hit TV and payment goes on the stack and you hit enter then your number your payment is automatically stored in this variable here so I can I can literally take this guy and if I want to multiply by five let’s say what AM what am i how many how much money am I going to be paying after five months then I can do that and I can work with it directly so the secret if you want to call it that is going into the finance menu going into the solver and typing in everything correctly and then basically putting the variable I mean the cursor on the variable you want let’s change it back to 360 so we went back in here to the calculator and typed in 360 again and we’ll see that our payment is going to stay the same because we really nothing’s changed so forty nine ninety eight per month now what if you want to calculate what is the principal and interest that you’ve paid on this loan up to a certain date maybe you’re curious how much interest am I actually paying after a certain period of time so if I quit here and I go back to the finance menu whoops wrong thing if I go back to the and apps and finance and I scroll down this a little bit and I’m gonna find some too pretty interesting things I have this is the some of the principal and the some of the interest that I’ve paid on the loan so it’s it’s pretty enlightening to look at this first let’s look at the interest what if I want to look and say okay how much interest have I paid on this because know your monthly payment part of it goes to paying the principal part of it goes to paying the interest so in the end you’re paying a whole lot more money than then you might guess so what about how much interest am I gonna pay after after ten months or a let’s say after the first twelve months so what you do is you have to tell it between what two months you’re keep you’re talking about so what about between the first twelve months between month one and month 12 what is the total sum of all the interest I’ve paid and the answer to that is fourteen thousand nine hundred and sixteen dollars it’s negative because I’m paying it out now it’s using all the variables that are already set up in your TVM solver so whatever you typed in there the interest rate the number of payments that value of the house all that stuff is basically applying to this calculation as well it’s just going in and figuring this out let’s go back and find out I’ll go second entry instead of instead of one to twelve months let’s say how much interest of my paying on the entire loan one two three hundred and sixty months so this is going to add up all of the interest payments that I make for the entire loan and the answer is two hundred and eighty nine thousand dollars that is how much money I’m paying an interest now the comb cost is only 250 so I’m actually paying more money and interest than I am just for the house so at this point I’ll I’ll take I’ll take it upon myself to show you that if you go back to the apps menu and go back to Finance and scroll down again then instead of instead of the the interest I can look at how much money I’ve paid towards that principle from month one you know we can go to month one to ten let’s say how much money or actually is make it the same let’s make it twelve so between month one and 12 I’ve only paid three thousand dollars toward the principal on this house the way interest works for such a large purchase like a house is in the first few years almost every dollar you pay them is going into their pocket in the form of interest eventually you’re gonna knock down the principal enough when you barely slowlyslowly pay it off so that the principal will come down enough and then you’ll start to pay the house off in substantial margins toward the end of your of your house note toward the end but you can see that between months one and twelve I paid three thousand dollars toward the value of the home I bought but I’m paying you know huge amount more just in the pockets of the bank because they loaned me the money now another thing you can do let’s go and change this I’m just curious more than anything let’s put this in here and let’s put the sum of the principal 360 whoops 360 and close the parenthesis off and you’ll see that I’ve paid two hundred and fifty thousand dollars which is exactly what I should have paid so the sum of the principal that I paid over the entire term of the loan is the value of the house so that that checks out now one more thing you can do by going in the apps menu there’s another interesting cool thing by going into write by some of the interest is a is a little function called balance be al number nine there so balance so what I do here is I put in the number of months I’m interested in and it’s going to tell me how much money I owe on this house so if I look after you know one month you got to put it in terms of month and when I put it in terms of one month I still owe almost the entire value of the house two hundred and forty nine thousand but if I go in here and I look after twelve months it hit enter look at this I only paid just like a minute ago we saw that we only pay about three thousand dollars in toward the principal and that’s roughly what we still owe we’ve only paid three thousand dollars of it off but we owe everything else after an entire year of paying on this thing now if I go in if I want to look at let’s say five years instead of typing in months I can just do five times 12 because I’m too lazy to type in 60 let’s say and I hit enter then I still owe two hundred and thirty two thousand dollars on this two hundred fifty thousand dollar house after five entire years of paying on it so it’s very slow to be paid off in the beginning now if you go in here and you type in five times so it’s a thirty year loan let’s say it let’s let’s look at year number 20 ventually at your number 20 things start to come down a little bit but look I still owe whoops I didn’t do the wrong thing there and did the wrong thing they let me pull that back up let me go over here it’s not 5 times 20 it’s it’s 20 is what I’m trying to do here 20 years times 12 that would give me the number of months for 20 years out so that’s what I’m trying to do I owe one hundred and thirty-five thousand dollars after 20 years that’s how much I owe and of course just as a final check to make sure you know what you’re doing here it was supposed to be a 30 year loan so if I put 30 in here should do delete insert 3 so 30 year loan 30 times 12 is gonna give you the number of months I should owe you know 3 bucks so the loans basically paid off so that’s that’s how you use this guy to evaluate mortgages you go in here you go to the finance menu you input all of your information in the TVM solver and then you have these little functions that you can use to calculate the principal calculate the interest calculate the balance if you can get good at using this calculator then I am absolutely convinced that you can walk into a car dealership and save a significant amount of money I don’t know how many times I have walked in and they don’t understand that I know a few things about math and so they’ll try to convince you that something’s cheaper but it’s very easy to show that it’s actually not cheaper and you can easily look at different interest rates different terms different down payments and figure out what is going to be the cheapest thing for you in the long run and so that’s a great introduction to using these these functions in the calculator I’m Jason I hope you’ve learned something I think it’s it’s a great little section to to really understand how money works and it’s a great time-saver as well

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