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3-27 AIM3 7.10 Monthly Payments

Added Mar 27, 2024 •

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hey there great news you're such a wonderful person we're going to buy you a car and we're going to figure out what the payments are so let's just see what's going on here all right well we got a great deal $9,000 the interest rate of 85% per year to that mind that's an annual rate you will be making payments every month so we won't be paying 5% interest a month that we'll figure out what we're going to pay all right I'm going to pay it off three years so what's it what's the payment going to be even luckier every now and then you might have seen and commercials dealerships offer 0% specials meaning they won't charge you any interest that you can if you borrow the money from them $1,000 doctor's going to pay back $9,000 will look at that and another situation where you do pay interest but let's just see what's going on here so does the recursive definition make sense at the beginning of the time that's before you make payment you owe $9,000 yet that that makes sense and your balance at any given time will be the previous balance and you been making a I meant I don't know if I said that will work and make a payment of $250 very much have 250 bucks we could figure out if you can get something paid off in 36 months and since there's no interest it's a very record calculation configure off 250 bucks a month how much would you pay in 36 months I have a question for you what would this recursive definition look like in our calculator so you might want to pause while you enter this in your calculator to remind yourself of how to do it then come back and see what I have alright so what's your initial value your time zero that's our first input what's our rule or rules can be the previous balance mom never got to subtract 250 and what's on your show output 9000 do we put that in our machine get our table star 0 increased by ones and we can see how long it will take to pay this thing off did you come up with the closed form for this particular situation again you might want to pause work on it and come back and see what I have well in this case it's pretty straightforward again because there's no interest your balance at anytime after say 0 months well you originally oh 9000 you can make a $250 payment every month so after 20 months that is the first day you still owe 9000 after one month without you pay 250 after 2 months you paid to 250 if you paid 500 so that's fine but let's look at something it stops more than what you're really going to deal with so let's see here again you're going to I borrow at 5% so that's fine but this again is keep in mind this his annual this is your yearly rate that's not what you're going to pay every month I'll be horrible to pay 5% of your balance every month that wouldn't nobody would have a car so what we have to do is take into account how much we're going to pay every month and it's pretty easy to calculate actually if it's 5% a year and you wanted to buy that in twelve parts well here you go right here you're at your monthly interest rate is 2.05 / 12 okay now that's fine but then what is it that actually determines what your balance is cuz you know subtracting 9:50 so let's think about this for a second you bought some money and then interest growth after that first month you don't know actually owe 9000 year old bit more 9000 cuz you're paying them interest to borrow the money and then you're going to make a payment so put it in in word form you are New Balance after any at a particular month is simply whatever the previous balance was you're going to add on interest and you subtract a payment and that's what your new balance is so the next month you'll take that new balance and on the interest on the current balance subtract the payment now you got your next New Balance so how can we defined that in terms of recursive well this isn't surprised the beginning we owe 9000 now what happens every month well our balance is based on the previous balance and then we're going to add the interest number the interest is per month. 105 / 12 * the previous balance how much do you currently owe and then you make a payment of $250 and that will determine your new interest so let's just make sure we got a previous balance interest and then you going to make payment and you can make a table and see how much you would owe at the end of each month and how long it would take you to pay it off and I certainly hope you're comfortable putting this into your calculator and so let's just follow up on that here so at the end of the first motor example you owed $9,000 that's what you borrowed then we need to add 5% / 12% off of $45 so you don't know 9000 you oh 9000 4583 do you make it payment 250 well that's why it didn't go down by $250 because you had gained some interest so the next month I'll start off at 8780 7:50 add 2.05 by by 12 times that make payment 250 this time of course because you're starting bounces a bit lower your interest will be a little bit lower it's your $250 will go a little bit further you'll pay a little bit that total 250 so let's look at our definitions here so is this is what we talked about a minute ago there it is you start at $9,000 paying off we're paying off $250 a month at a 5-4 monthly right there is and what do we have here well in our calculator I hope you would see this we started 0 previous balance plus by 12 of the previous balance - 250 and our original balance was $9,000 so you be able to use this answer the questions we're playing around with today have fun

Uploaded by Brian Macky.

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3-27 AIM3 7.10 Monthly Payments

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