watch casio calculator

welcome to our finance unit. we'regoing to start out our unit today by talking about a very powerful financial tool - and that tool is interest. interest is generally given to youas some type of a percentage rate and we're interested in what ishappening to your money over time. keep in mindevery time we talk about interest - sometimes interest is a bad thing - like when you're paying on a loan. sometimes interest is a good thing -

like when you're putting money in asavings account. either way, the calculations are fairly similar whether you are paying interest or gaining interest. hopefully we'll talk about theadvantages that the system both ways here. when we start our little adventure herein interest land, we are going to start by discussingsimple interest. simple interest is where you just

have -- or, you're making some sort ofeither an investment or a loan, and you are going to have a particular percentage of return for that moneythat you're putting in. the basicidea of simple interest is that there is just a flat percentageinvolved. so, let's say for example that, we'll use my son, evan, because he just did this the other day. his little brother wanted to buya video game, and evan had some leftover birthday money.

and so he went ahead and said "i will giveyou the five dollars that i have, but when you pay me back you need to payme back with 10 percent interest." so he's, you know, holding this over his littlebrother's head. so his little brother is 7, and he wants that five dollars, so he'sgoing to go ahead take up evan on this deal. so, if this is all that we're talkingabout, then if we want to figure out how much interest his little brother has topay, all we do is we take that five dollarsand we need to figure out what 10 percent of five dollars is.

so we take the five dollars and we multiply it by 10 percent. remember, when are dealing with formulas we always need to change thosepercentages into decimals. so it would just be five dollars times 0.10. you can do it on a calculator if it's notsomething it could do in your head, and in this particular case i get .5. since i'm dealing with money, thatwould be .5 or 50 cents and and this is the amount of interestthat he's charging his little brother for that particular loan. fiftycents

in interest is how much he owes, so thetotal amount that his little brother would have torepay is of course the five dollar loan plus the50 cents of interest. so a total amount at five dollars andfifty cents. so this is going to be real similar to thatfirst homework problem that you have. it just gives you a flat amount. it gives you a percentage of interest thatyou are needing to repay. and it's just basically a percentageproblem - where you multiply the amount by the percent written as adecimal and you can get your total.

that's really the basics for what there is in terms of simpleinterest. the next piece that we have is sometimes this. obviously there was norepayment deadline here - evan didn't say he'd have to pay me backtomorrow or next week or next month. he just said pay me back, and this is howmuch you have to pay me back at the end however, banks don't really like to workthat way. they want you to pay them back as soon as possible. so they put alittle bit of a time stigma to it. so how does that all work out?

most banks actually use something called compound interest which is a little bit more complicated. but there is one government entity, believe it or not, out there that actually deals with simpleinterest. the federal government will give outtreasury bills, or treasury notes rather, and we call them t-notes, and the t-notesactually use simple interest. it's a type ofbond, the book goes into a kind of better

explanation for it, but let's suppose that we have, let'ssay, a two thousand dollar t-note that we take out. and we take it out with let's do 5 percent interest. this interest is going to be given to usas an annual rate, and they usually are given as interests. interest rates aregenerally given as annual rates and that's something that

had changed in the last twenty or thirty years as people realized that it's hard to compareinterest rates if you don't have a standard comparison time. so this is saying 5 percent every year. now, the idea with a t-note is you're going to give the government this two thousanddollar loan. they're going to pay you back five percent - at a five percent annual rate, and they'regoing to pay back. sometimes they pay back every quarter -

so every three month they're going to pay you a portion of whatever interestyou've earned. now keep in mind if they're paying youquarterly, that means that they're paying you four times a year. you are earning five percent interestannually - so if we are being paid quarterly, we're not earning all of that interest. we are only earning a fourth of that interest when we're talking about simple interest. and so we can actually kind of figureout exactly what percentage of interest

we get, and we can figure out how much interest you get paid thatfirst three months. and then three months later, you get that same interest paymentagain. three months later you'd get that same interest again. and then what's going to happen is, eventually, our t-note is going to come up due. we call it "maturity" and that's basically when thegovernment has to give you their loan - the amount of money that you borrowed - back. so let's say that this is a t-note that has maturity in threeyears.

so what that means is you're going toget paid four times the first year of interest, four times the second year in interest, four times the third year in interest. you're going to end up with twelveinterest payments, and then at the end of the twelve months,you also get your original two thousand dollars back. so that's the way that t-notes work. now, in the book they go to a lot of troubleabout figuring out what this, if you're getting paid quarterly,dividing the interest rates, all of that

exciting stuff. but, at the end of the day, simpleinterest is simple. and you don't even need toget nearly as complex as what the book was actually asking you to do here. the formula that we use to calculatesimple interest is this: "i" equals "p-naught" (or this little p-zero, we often call p-naught) times "r"times "t". now what do each of these things stand for? the i stands for interest of course - that's what we're talking about.

p-naught, or p with this little 0, is our starting amount or our principal - sothat's our new economics term for the day. principal is just the starting amount in youraccount if you are starting a savings account, or it's the starting amount of your loan - how much money you borrow. this is not a multiplication, it'snothing else, that little 0 here just means that it'sthe starting value and a lot of times you'll hear the word p-naught

it's just like an old british term for zero, but it's fairly common discussion notation. "r"stands for the annual interest rate, and as long as youput the annual rate in here you're going to keep yourself out of trouble. and "t" stands for your time. and as long as you keep your time in years, you're going to stay out of trouble as well. so i'm going to simplify the problem that you have in your homework a little bit by just saying that the example thatthey have for the t-note in the book

is little bit unnecessarily complex. as long as you use the annual rate and your t is in years, you don't haveto worry about dividing the interest rate and all of that crazy, crazy stuff. so we're just going to use this formula if i want to figure out the total amount of interest i'm going to getfrom this t-note, i can go in and and say "okay, i want to findthe interest. p-naught is my starting amount which in this case is two thousand dollars. my r is the five percent, and justremember that you always have to write

those percents in decimal form. and my t is how many years i'm going to keep this t-note in production - and in this case its forthree years." and then, if i want to get the interest, ijust want to multiply those values together. so coming over here we have twothousand dollars times by .05 for my five percent times by three years. and at the end ofthe day, i'm going to have ended up earning three hundred dollars from myt-note investment and that's the amount of interest that iwill have earned at the end of that

period of time. so, kind of cool. a lot more simple thantrying to divide and then figure out how many payments there are - and so on. if you actually wanted to figure out how much interest you'd have have gotten during each of these payout periods, you could just divide by how many. therewere 12 payouts, so you could do 300 divided by 12 and you could walk away and say"ooo, now i get twenty-five dollars everythree months until the end, and then i

get my two thousand dollars back at theend three-year period. so that's the way thatt-notes work. this is our special, magic, lucky, simple interest formula for when we're talking about simple interest. now keep in mind, most banks have a different method of doing stuff. the federal government is one of the fewgroups that actually does use simple interest for their calculations. so when we see these t-notes we arealways talking about simple interest and can just use this real simpleformula: how much you're paying

times by the annual interest rate times by t which is the number at years when we are trying tofigure that out. alright. so that will get you through the first two homework problems. the next two homework problems come upwith or start talking about a new type of investment. it's not called atreasury note, it is called a treasury bill. so if we are talking about a treasury bill, this is a little bit different than thetreasury note where you'd give an amount

they'd pay interest on it, and then theypay you the original amount back. the idea with the a treasury billthat you're going to start out with a certain - you're gonna basically say"okay. i want to have five thousand dollars at the end of this, but i am going to get this - i'm going to pay maybe four thousandfive hundred dollars at the beginning. so i'm going to make an investment of $4500. i'm going to give that to the government and at the and of whatever my maturity period is (sohowever many years later) they're going to

give me five thousand dollars at the end. so a little bit different than whathappened with the t-notes where are you getting payments every single way along the way, and then you get your originalpayment back. here, what you're doing is you're buying something at a discountedrate and they're going to give you anadvanced rate at the end of that period of time. in the last problem, we used this formula i = p-naught * r * t, and what this gave uswas just how much interest we earned.

if we'd like to figure out how muchtotal amount something is worth, we use a slight variation on this formula. it's just the total amount that youearn is just what you started with plus your interest.now, using a few other things, we can kind of put this all together and we end up with this formula that's really the useful one here that theygave you in the book, and that's this: a is the final amount have money that you have

at the end p-naught, of course, is that initialstarting value or your principal. "r" is still (oof - principal, that's spelled really well there - there we go). "r" of course is your annual interest rate -- and againit's real important to stick with that annual thing. and as long as they give it to us in that form, we're happy. and t is the number of years.

sticking with an annual rate here and atime in years is going to be what keeps you out of trouble. so we can use this formula here to getstraight to the answer that we want. now when we're talking about a t-bill,let's suppose that we have - that we're going to buy a two-year t-bill. we'll just do this one here. we're goingto say that we're gonna buy it at $4500 and two years later the government'sgonna give me five thousand dollars for it. my question is, what interest rate wouldthis be equivalent to?

how much interest was i earning? in order to figure this out we can usethis formula here. basically what's happening in thisproblem is: i want to end up with a total of $5000. so i'm going to put 5,000 in for a. p-naught is my starting orinitial value - in this case, i started by taking a fortyfive hundred dollar loan out from the government -- or rather giving a $4500 loan to the government, i guess is a better way to say it. and then we are going to multiply that times 1 plus my interest rate -

which i don't know - times by my time, which isthe number of years and in this case i'm talking about a two year period. sowhat i have here is 5,000 equals 4500 times 1 + "r" times 2. you'reprobably going to keep yourself out of trouble just a little bit if you go ahead andwrite that as one 1 + 2r. you are a little bit more used to seeingthings that way, and more likely to do the mathematics correctly if you take thetime to do that. now, at this point what i'd like to dois i'd like to solve this equation.

so, first of all, notice that my "r" is stuck inside the parentheses. so if i'd like to get it out, i can usethe distributive property to multiply this out. i get 5000 = 4500 * (oops, just kidding), use the distributive property 4500 times 1 is 4500. plus 4500 times 2r is 9000r. now if i'd like to solve this, the nextthing that i'm going to do: i need to get the "r" by itself.

i have to get rid of both the 9000the 4500. i am going to minus the 4500 first from each side. that's going to leave me with five hundredhere. equals 9000r. i want to get r by itself, so i'm going to divide both sides by 9000. that gets the r alone. and then i'm gonnado 500 divided by 9000 because i don't know whatthat is my head, and i end up with r equals .05555 we'll just round it to 4 decimals here, so .0556.

so that's my r. now remember r is myannual interest rate, however, because i got r out from aformula, remember that formulas always deal with rates in decimal form.so if i'd like to talk about what interest rate that is, all i have to do is move the decimal 2 places to theright and i can say r is equal to 5.56 percent. so this particular investment, by buyingthis discounted $4500 account t-bill, i'm essentially earning 5.56%

annual interest, and at the end of twoyears i would have that five thousand dollarsin terms of what they give me at the end of it. the last way that - um, so that's kind of similar toproblem number three on your homework. the last type of problem (oh, i didn't want to save that - let's try that again sorry about that. ok. so here's my blank page).

the last like a problem that we haveis let's suppose that we want, we're looking at t bills again, and let's suppose that we want to get at-bill that at the end is going to be worth five hundreddollars. so that we call that a five hundreddollar face value. and let's say that this is a 13-week bill. so 13 weeks later i'm going to get this fivehundred dollars and i would

like to i would like to do what? i would like toearn 2 percent interest so at the end up thirteen weeks iwant to have five hundred dollars. i need to have earned at least 2 percentinterest. and my question is: how much with i have to pay in order to make all of this work. so in this case, again, we're dealing with this t-bill problem

i'm going to want to use this formulaa = p-naught times 1 + rt. in this case i want to end up with fivehundred dollars - so that's the ending amount. and what i'm looking foris how much i would pay up front in order to get that to happen. so whati'm looking for is, i'm looking for p-naught this time, which is little bitdifferent. now, this is going to be times 1 + r, the interest rate i'd like to earn is 2% annual interest, so .02 times by t. now

t, remember is the time in years, unfortunately i'm given the time in weeks. so you haveto kind of deal with things a little bit if i have thirteen weeks, how many yearsis that? well, keep in mind that there are 52 weeks in a year. and so if i take my thirteen weeks and idivide by 52 weeks, my units will cancel and i'll be left with the number of years. so i'm going to take that thirteen and divide it by two or 52 rather - and when i go to put in mytime in years, and in this case,

my time in years, 13 weeks is a fourthof a year. so the t value that i'm going to use inthis problem is .25. awesome. okay, so i've set up my formula. i don't know how much i'm starting with, but i want to end up with $500. i'm going to be earning 2 percent interestand i'm going to have it in this investment for only a quarter of a year, so .25 years. so that's where each of these pieces ofinformation comes in. alright, now keep in mind that everything inhere right now in these parentheses is

just a number. there's no variables in there, so i can just go ahead evaluate that: 1 plus .02 times by .25 and what i get there is 1.005. so i have 500 is equal to p-zero times 1.005. i want get the p-zero by itself so i'mgoing to divide by 1.005 on each side, and that will get me my p-naught, orstarting amount. so i do 500 divided by

(oops thats only 50, try again). 500 divided by 1.005, and i and up with: at the beginning of this time period for a 2 percent interest over just that very short period of time of just thirteen weeks i would have tobuy a 497 dollars and 51 cent starting investment. so, not earning awhole lot of interest there but then again, 13 weeks wasn't a whole lot of time and 2%

isn't a whole lot of interest when aretalking about about stuff. but that would be howmuch initial money i'd have to put in in order to make that t-bill work. again, we've just been dealing with simple interest, and simple interest is of course thesimplest - just dealing with the a flat percentage. we're going to put money in, time is going to go by, we are going to earn that percentage back. or if we're borrowing money from thegovernment, they kind of do this nice

simplified thing, and when we're dealing witht-bills or t-notes, which are treasury bills andtreasury notes, they're dealing with simple interest. when you're dealing with simple interest, this is the magic formula you want to use. or if you just wanna know about theinterest you can use this i = p-naught times r times t. if you want to know total amountsyou're dealing with, use this formula. so these are the only two formulas toworry about. again, don't worry about

all the weird complexities that the booktells you. as long as for r you using an annual rate andfor t you are using time in years, you don't have to worry about adjustingrates and all of that crazy stuff that they tell you in those couple examplesthere. so simplify your life little. give that a whirl. if you need anyfollow-up questions, please ask them on the discussion boards, and we'll see you in the next video.