Installment Buying, Unearned Interest, Finance Charges, APR - YouTube

there are two types of installment loans. one is called a fixed installment loan.

this is like a loan that you get to pay off a car where there's a preset number

of months and you pay the same amount every one of those months. the next type

of installment loan is called an open end installment loan. these are like

credit card loans where you make a different payment every month and

there's no preset number of months for which this loan needs to be paid back.

all of these loans have finance charges which just means the total

amount of money that you're paying to borrow this money. and in a lot of these

problems we're going to be using an annual percentage rate, or APR, which is

like a simple interest rate, but it's used to compare one loan to another. now

that we've got some definitions written down let's take a look at our first

example. let's determine the monthly payment on a loan of $10,000 over five

years with a 6% APR. to do this we're going to use the installment payment

formula. so get ready for a complicated formula. now for this formula M

represents the monthly payment. P is the total amount borrowed. R is the APR

interest rate that of course needs to be written as a decimal. T is the time in

years. and n in this case is the number of payments that you're going to make per

year. pretty frequently our n value is going to be 12 because you're making

monthly payments. so in this problem we are borrowing a total of $10,000 -- that

means P is going to be 10,000. our APR is 6% so that R value is going to be point

zero six. we're taking this loan out over five years so T is going to be five. and

this is a monthly payment so our n value is going to be 12. if we take all of

those numbers and plug them into this formula here's what we get. plugging all

this into our calculator can be a bit of a chore, so let's go through it step by step.

let's simplify what's in parentheses in the numerator by dividing point zero six

by 12. okay that's point zero zero five. in the

denominator let's simplify the one plus point six over twelve in parentheses

that's one point zero zero five. and let's also simplify the negative 12

times 5 that's negative 60. now let's give ourselves a little bit of room here and

continue the simplification. the numerator is now ten thousand times

point zero zero five let's see if we can enter that in.

I'm getting 50 for my numerator. let's next try to calculate one point zero zero 5

to the negative 60th power. for this little piece my calculator is giving me

0.74137 I'm gonna take as many decimal places as I can here. now let's

simplify the denominator by subtracting that number from 1. that gives me 0.25 8

6 2 7 8 in the denominator. now let's finally get our value for M. our monthly

payment by dividing 50 by this result. I'm getting a hundred and ninety three

dollars and 33 cents. that is a pretty good answer let's try to do the same

problem just a different way we're going to determine the monthly payment on the

same exact loan but this time we're going to use this table. this annual

percentage rate table for monthly payments. the first thing that we want to

do here is look up our APR in the table. we're gonna be looking at this column

right here now a 5 year loan is how many monthly payments. well five years times

12 months per year gives us 60 monthly payments. what that means is we need to

be looking at this number here in the table, and what this number gives us is

the finance charge for taking out this loan for every $100 that we borrow. so

how many hundreds of dollars are we borrowing? well, we're borrowing $10,000.

if we want to know how many hundreds that is we can divide that by $100. that

gives us that we were borrowing a hundred $100 increments. we are

charged 16 dollars per increment, so our total finance charge for taking out

this loan is $1,600. so we're borrowing $10,000 and we have a $1,600 finance

charge on top of that so ultimately over the course of these five years we need

to pay back $10,000 plus the $1,600 which comes out to be eleven thousand

six hundred dollars. now if you're still with me here we have one more step. this

$11,600 needs to be paid off over the course of 60 months. so if we take that

11600 that we owe and divide it by 60 months we get a hundred and ninety-three

dollars and 33 cents as our monthly payment. and you'll notice that that is

the same monthly payment that we got in the previous problem. we'll need to

know how to do these calculations using both of

these techniques. so take another good look at that make sure that the steps

make sense and then let's move on to this next problem. you're buying a used

car that costs eleven thousand dollars. you can make a down payment of four

thousand and you'll be making thirty six monthly payments of two hundred and

twenty two dollars. the question is what finance charge are you paying?

well again the finance charge is how much money you're paying just to borrow

the money, so the first question I would ask is "how much are you actually

borrowing?" well your car costs $11,000 but you're making a down payment of

$4,000. that means that you're immediately paying $4,000 towards the

car leaving only seven thousand dollars that you're financing. okay that'll be

good to know. next let's find out how much you're actually paying over the

entire course of this loan you're gonna make thirty six payments and each one of

those payments is gonna be two hundred and twenty-four dollars. so you're paying

a total of $8064. so you're borrowing seven thousand dollars but

ultimately you're paying eight thousand sixty four dollars. subtracting those two

gives me one thousand sixty four dollars, and that's how much your finance charge

is. if we now want to find your APR, what we need to do is find how much you're

paying in finance charges per 100 dollars that you borrow.

well we're borrowing $7,000. that is seventy times 100 dollars. so if we want

to know how much we're paying in finance charges per 100 dollars that were

borrowing we divide our total finance charges by seventy. and that is giving me

fifteen point two dollars or fifteen dollars and 20 cents. now I'm realizing

that this table that I gave you is not enough, so I'm gonna get rid of it and

replace it with one that we can actually use. we're gonna look up this $15.20

in our table in the row with thirty-six payments. when we do that we see that the

closest number to fifteen dollars and twenty cents is over here and that gives

us an APR of approximately nine point five. okay so that's the answer to the

second part of that question. now we've got a couple of pretty tough problems

coming so let's take a look at the next one. you take out a 60 month loan for

twelve thousand dollars and make payments of two hundred and thirty-two

dollars per month. instead of making payment number 36 you wish to pay off

the loan. first let's determine the APR of this loan. we're gonna use this

table over here to determine the APR but before we can do

we have to figure out our finance charges. so how much do we expect to pay

for this loan first? we're paying two hundred and thirty two dollars per month

for 60 months multiply those numbers together and we get thirteen thousand

nine hundred and twenty dollars that we expect to pay. and if our original loan

was twelve thousand dollars that means in finance charges we are paying

nineteen hundred and twenty dollars. to use this table though we need to find

the finance charges per 100 dollars borrowed. well how many hundred dollar

increments are in twelve thousand dollars if we divide twelve thousand by

100 that is a hundred and twenty increments. so we're going to divide

$1920, our total finance charges, by 120

increments. that gives us that our finance charges per $100 borrowed is

sixteen dollars. now if we look up in this table in the sixty month payment

row we can find sixteen over here. that means that our APR is six percent. the

next question asks us to find how much interest we're going to save by paying

this loan off early. again instead of making a payment number thirty six we're

going to pay off the loan completely, so get ready for a formula. this is called

the unearned interest formula. this is interest that goes unearned by the bank

U represents that unearned interest. N is the number of payments you're

making per year. T is the monthly payment. and V is a little bit of a tricky one...

we're going to get V from this table up here. we are going to use the six percent

APR column but we need to look at the row that has the number of payments that

we have left. the number of payments we have left it's just going to be 60 minus

36 which is 24 so we have 24 payments left (if we exclude that payment number

36). so we look up in this table under number of payments we see 24 is our row.

we have this number 6.37. in that is going to be our V. so how do

we summarize this V? It is the value from our Apr table corresponding to the APR

and the number of payments that you have left. okay so let's go ahead and plug the

numbers for this problem in. our number of monthly payments per year is 12 our

monthly payment was two hundred and thirty-two dollars for this problem and

the value that we got from table was six dollars and 37 cents. in

the denominator we have a hundred plus the 6.37 from the table. plugging all that

into my calculator is giving me a hundred and sixty six dollars and

seventy two cents. that is the amount of money that we're saving by paying this

loan off early. for the final question we're going to determine the total

amount due to completely pay off this loan. so instead of making our 36th

payment, we're going to pay the total amount due. well from the first part of

this problem we found that the total amount of money that we expected to pay

for this loan was thirteen thousand nine twenty. the total amount that we paid so

far for this loan is our thirty five payments of two hundred and thirty two

dollars. so far we've paid eight thousand one hundred and twenty dollars

for this loan. we also know that we're saving one hundred and sixty six dollars

and seventy two cents by paying off this loan early, so how much do we have left

to pay off this loan? well it's gonna be that thirteen thousand nine twenty minus

what we've paid so far minus the savings that we're going to make by paying off

the loan early. I'm getting fifty six hundred and thirty three dollars and

twenty eight cents as the total amount that we owe on this loan. okay we have

one more it's another tricky one. on February 2nd, that's the billing date,

Carol Anne had a balance due of 129 dollars and 21 cents. she made the

transactions described in the table during the month so you can see over

here that Carol Ann made three charges and one payment. we're gonna determine

the finance charge if this credit card company is going to charge Carol Ann on

March 2nd using the previous balance method, and then we're going to determine

the new balance. the previous balance method is kind of what it sounds like --

credit card companies typically only charge you interest on your previous

balance. so if we want to figure out how much interest is charged to Carol Ann

all we have to do is look at her previous balance. and we're basically

just using a simple interest here the interest charge is the principal times

the rate times time. that previous balance is going to give us a principle

of one hundred and twenty nine dollars and 21 cents. interest rate is one point

two five percent per month so we convert that to a decimal. and this interest has

accrued over the past month that means that the interest charged to Carol Ann's

accounts is going to be one dollar and sixty two cents if we round up. Now, as ar

as Carolyn's New Balance goes we just need to add and subtract everything up.

we started with $129.21 cent balance. we're going to add to that

a dollar sixty two finance charge. Carolyn also charged $20.65

she then made a payment of a hundred

dollars, thus reducing her balance. and then she bought sixty seven dollars and

fifty one cents worth of flowers, and CD for ten dollars and 22 cents. and okay,

that was a coincidence I added all those numbers up and got that her new balance

is the exact same thing as her old balance. okay that was a long one had a

lot of formulas in there. this would probably be a good video to watch a

couple of times. go back and take another look. the next video is about mortgages.

I'll see you there!