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Business Math Sem 1 #82

All right students you’ve done it you’ve taken the plunge and you’ve bought a super computer that can help you do all types of amazing things for video editing you didn’t have 2 000 of the dollars to pay for it so you had to take out an installment loan and you know that every single month you’re going to pay the same amount let’s take a look at what the

Implications of this are and how much of that monthly amount you are sending to the bank in terms of how much you owed and how much you owed in interest so down here we need to borrow 2 000 to buy this computer the original amount you borrow is called the principal so this is the original amount borrowed but i think what i might just say here is amount

Owed just to make that easier on all of us amount owed okay so you owe somebody two thousand dollars for um for basically they gave you two thousand dollars to to buy this awesome computer and you said you’ll pay it back in three years over three years in monthly installments at an interest rate of 12 percent and what they say is they they’re like okay well

We’ll create a table for you and based on this amount this time frame and this interest rate we can give you monthly dollar monthly payments of 66 so as long as you pay us 66 every single month for three years you’ll have paid off the entire two thousand dollars and your interest and you’re saying to yourself okay hmm let me cover up this last part so it’s not

Distracting us you say to yourself well how much of my first payment is going to go to interest and how much of my first payment is going to go to principal because ideally i want to pay off this amount as fast as possible i don’t want to just be paying interest for the rest of my life so two thousand dollars is how much we owe and we’re going to pay 66 back

Every single month but some of that is going to be interest how does this even work well in your first payment your first payment you’re going to be paying 66 and some of this goes toward interest because you owe 12 interest on 2 000 and some of it goes to pay down the principal of that 2 000 that you borrowed how do you figure out what the split is for your

First payment well you know it’s 12 right you owe 12 you know it’s a monthly payment and there are 12 months in the year so this is just one out of 12 months that you’re going to owe this and you know that since this is your first payment you haven’t paid any principal off right so you’re going to actually owe the full 2 000 of 12 interest for that one month

So what do we do here we’re gonna multiply by the full two thousand dollars that we owe so twelve percent times the twelfth times the two thousand dollars in principle or the amount that we owe will give us our first split of interest the remainder will be how much we paid off in principle so 12 times a 12 is just 1 why well 12 over 1 times 1 12 would give

You 12 over 12 and anything divided by itself is one so we have one percent of 2 000. you say oh one percent i could do ten percent one percent sometimes gives me some trouble well ten percent just divide by ten that that’s simple so you divide by ten you get two hundred but we want a tenth of that so divide by 10 one more time because one percent is a tenth

Of 10 so 200 divide by 10 one more time we get 20. so this is 20 dollars in interest right because this 12 is the interest rate so this is how much interest we pay on our first 66 dollar payment that means the rest of it goes down to pay our 2000. so 20 less than 66 gives us 46. all right so of this 66 initial first payment 20 of it goes to interest because

We borrowed 2 000 to buy this computer but 46 of it goes to pay off the principal and so what’s really cool is that we can subtract now that 46 dollars and now we only owe 1954 dollars in principle so the principal has decreased for the second payment which means we’re actually going to owe a little less interest because instead of multiplying one percent by

Two thousand we’re going to multiply one percent by 1954. now if this was twenty dollars one percent of this will give us nineteen dollars and fifty four cents so you can see that as you chip away at the principal you’re actually paying less in interest which makes sense let’s go to this second piece of the problem that was for the first payment on the 24th

Payment so after you’ve been paying off this computer for two years your outstanding principle has decreased all the way to 806 dollars that’s awesome you used to owe 2 000 and now you only owe 806 because you’ve been paying off some of your principal every single month so now you can actually do the same calculation and say well how much in interest is this

66 and how much in principle is this 66 dollars so the interest rate hasn’t changed and the month hasn’t changed right it’s still the same 1 12 of a year so we’re going to pay 1 of 806 so we know that we started off in interest on two thousand dollars our first interest payment was twenty dollars and then it went down to nineteen dollars and fifty four cents

So now after two years our interest payment has decreased all the way to eight dollars and six cents super cool as you chip away at that principle and you owe less and less money you’ll pay less and less interest so of this 66 interest will be 8 and 6 cents and principle will be the remainder eight dollars and six cents well let’s just do eight dollars and

Then we’ll take the six cents off that so 66 minus eight gives us 58 then we need to take six more cents off so 57 94. so you can see over time in installment loans you pay less and less interest from twenty to nineteen dollars and fifty four cents to eight dollars and six cents you’re paying less and less interest and you’re paying more and more principal

So that’s pretty cool you get an installment loan and it starts to get into your favor first you’re paying a lot of interest and not much principle and then over time as you chip away at that principle you’re paying more and more principle and less and less interest and that’s really what you want cause paying interest it’s not really interesting it’s it’s

Another it’s another business math joke it’s not really interesting because you’re not getting anything for it you’re just paying somebody for letting you borrow money so ideally you just want to pay the money back as fast as possible thanks for watching have a great day you

Transcribed from video

Installment Loans, Monthly Payments, Finance Charge 82 By SOESD Interpreted