pTI84 Calculator 36 Calculating Mortgages and Loansp phello and welcome to the section of the tutorial where were going to continue looking at financial calculations with the ti calculators and in this this chapter were 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 were paying more than the cost of the item thats just out how the world works so when you when you buy a house lets say your house cost a hundred thousand dollars you know and you take out a loan for thirty years youre going to pay a whole lot more than a hundred thousand dollars for that house of course the advantage to you is that youre doing it over 30 years that you can afford to make those payments whereas most people dont 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 lets go in the apps menu under finance the very first thing is TVM solver time value of money and I think this is eyeopening for most people until you sit down and start playing around with loan numbers you know you really its hard to imagine how much money people pay for houses and cars when we take out long loan so lets take a look at it what we have in here is a bunch of variables Im going to explain what they all are theyre very easy to understand but the basic idea is you fill out what you know and then the thing that you dont 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 lets say youre going to buy a house and youre going to take out a 30year mortgage so 30 years times 12 months is 360 months so youre gonna pay 360 payments and thats what n is equal to and actually I should have told you Ill do this now before we jump into here too far let me go out of here and go to the mode menu when youre dealing with money its a very good idea to get the float on two decimal places and that way everythings gonna look like a nice dollar signs coming out of there so well 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 youre gonna write over the entire life of the loan thats the number you put in there this number is the percentage rate interest so for this particular example lets choose 8 percent interest on a home this this number here is this PV stands for present value and basically thats the value of the home that youre buying or if youre buying a car its the value of the car so for now lets 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 thats what Im gonna actually calculate first so were not gonna put anything there FV is future value Ill tell you about that later dont worry about that right now its 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 its just asking you because the calculator has no idea what youre buying you have to tell it okay you told it youre 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 theres a line thats C y this means compounding periods per year so most of the time if youre making 12 payments your loan is going to be compounded monthly as well so its going to the calculator notice automatically put a 12 there I didnt even do that thats an automatic thing you can override that if you need to but thats thats the basic idea so I think now were pretty good to go this this tells you if youre 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 its 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 youre actually at a car dealer ship trying to figure out whats 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 youre hit alpha is because you have to hit the solve button right here and then notice that it pops out with a number theres a little square next to this which means the calculator has calculated the answer there as opposed to these other fields that dont have a square thats because you input these numbers yourself the calculator calculated this one and your payment is negative eighteen thirty four dollars and fortyone cents per month the reason its negative is because this represents money leaving your wallet so its cashflow leaving you so its why its 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 its 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 youre making these payments almost 1, 500 a month and youre 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 its 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 fortyseven 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 Im 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 fortyseven thousand four hundred fifty four dollars thats basically what it is so you can also use this in the in the positive sense if youre 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 isnt so thats what thats doing right there now one more thing I want to tell you is that the calculator once you make these calculations lets 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 lets 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 lets change it back to 360 so we went back in here to the calculator and typed in 360 again and well see that our payment is going to stay the same because we really nothings changed so forty nine ninety eight per month now what if you want to calculate what is the principal and interest that youve paid on this loan up to a certain date maybe youre 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 Im gonna find some too pretty interesting things I have this is the some of the principal and the some of the interest that Ive paid on the loan so its its pretty enlightening to look at this first lets 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 youre 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 lets say after the first twelve months so what you do is you have to tell it between what two months youre keep youre 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 Ive paid and the answer to that is fourteen thousand nine hundred and sixteen dollars its negative because Im paying it out now its 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 its just going in and figuring this out lets go back and find out Ill go second entry instead of instead of one to twelve months lets 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 Im paying an interest now the comb cost is only 250 so Im actually paying more money and interest than I am just for the house so at this point Ill Ill take Ill 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 Ive paid towards that principle from month one you know we can go to month one to ten lets say how much money or actually is make it the same lets make it twelve so between month one and 12 Ive 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 youre gonna knock down the principal enough when you barely slowlyslowly pay it off so that the principal will come down enough and then youll 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 Im 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 lets go and change this Im just curious more than anything lets put this in here and lets put the sum of the principal 360 whoops 360 and close the parenthesis off and youll see that Ive 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 theres 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 Im interested in and its 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 thats roughly what we still owe weve 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 lets say five years instead of typing in months I can just do five times 12 because Im too lazy to type in 60 lets 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 its very slow to be paid off in the beginning now if you go in here and you type in five times so its a thirty year loan lets say it lets lets 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 didnt do the wrong thing there and did the wrong thing they let me pull that back up let me go over here its not 5 times 20 its its 20 is what Im trying to do here 20 years times 12 that would give me the number of months for 20 years out so thats what Im trying to do I owe one hundred and thirtyfive thousand dollars after 20 years thats how much I owe and of course just as a final check to make sure you know what youre 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 thats thats 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 dont know how many times I have walked in and they dont understand that I know a few things about math and so theyll try to convince you that somethings cheaper but its very easy to show that its 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 thats a great introduction to using these these functions in the calculator Im Jason I hope youve learned something I think its its a great little section to to really understand how money works and its a great timesaver as wellp

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