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How To Calculate Your Monthly Mortgage Payment Given The Principal, Interest Rate, & Loan Period

in this video we're gonna talk about how

to calculate the monthly payment of a

mortgage so in this example problem

Jessica takes out a $300,000 loan at a

fixed interest rate of 5% to buy a home

the loan is to be repaid in a time

period of 30 years Part A calculate

Jessica's monthly mortgage payment what

is the form of that we could use to get

the answer the monthly mortgage payment

is equal to the principal P times the

interest rate R times 1 plus R raised to

the n n is the total number of payments

that need to be made

divided by 1 plus R the raised to the n

minus 1 so let's write that what we know

the principal is the mortgage $300,000

and that's how much she's borrowing to

buy the house now the interest rate is

5% but we'll need to convert that into a

decimal to do that you can move the

decimal 2 units to the left or divide 5

by 105 divided by 100 is point zero five

now this will be the annual interest

rate we wish to calculate the monthly

payments so we need to get the monthly

interest rate in this case because this

12 months in a year we need to divide

point zero five by 12 so that's gonna

give us our R value n is the number of

payments that will be made over the

length of the loan so Jessica took out a

30-year mortgage and it's 12 months in a

year so you need to multiply 12 by 30

which is there's 360 months in 30 years

so she's gonna make 360 monthly payments

so that's our end value

the only thing that we need to calculate

now is the monthly mortgage payment so

let's plug in everything into this

formula so P is 300,000 R is point zero

five divided by twelve and then it's

going to be one plus point zero five

over twelve the race to the N so we said

that n is 360 divided by one plus point

zero five raised to 12 I mean / - I'll

rather a race to the end again and then

minus one so let's do this one step at a

time

let's take 300,000 multiply it by point

zero five and let's divide that by 12

you should get 1250 next let's calculate

this portion type in what you see so one

plus point zero five divided by twelve

that's one point zero zero four one six

repeating and then raise that to the 360

power so you should get four point four

six seven seven four four three one four

so this is going to be the same as that

number

well there's no point in rewriting it we

could just subtract it by one so this is

four point four six seven seven and then

the rest of that stuff minus one so

that's gonna be three point four six

seven seven four four three one four

so 1250 times four point four six seven

seven four four three one four divided

by the number on the bottom will give us

our answer so the monthly mortgage

payment is one thousand six hundred ten

dollars and forty six cents the exact

value by the way for those of you who

might be interested is this number but

just to keep things simple I wanted to

round it to the nearest cent

so that's Jessica's monthly mortgage

payment now it turns out that there is

another formula that you could use to

get the same answer and it's formula is

a little less I mean it's a little more

simpler than the first one so it's P

times R divided by 1 minus 1 plus R but

raised to the negative n instead of

positive n let's try that form of 2 so

let's take the principal of 300,000 and

let's multiply it by R which is 0.05

over 12 and then from the bottom you

want to introduce a set of brackets if

you're gonna use a calculator so 2 1

minus 1 plus 0.05 raised to the 12 and

then I mean divided by 12 but raised to

the negative 360 so don't forget to

include the negative side it's very

important

so 300,000 times 0.05 divided by 12 we

know that to be 1250 and then

one - and then in parenthesis 1 plus

point zero five divided by 12 raised to

the negative 360 that's point seven

seven six one seven three four zero four

four so dividing those two numbers gives

you this answer as well so that's

another way in which you can calculate

the monthly mortgage payment so now that

we have the answer to Part A let's move

on to Part B calculate the total amount

of money that she will have to repay so

we know that she needs to make a total

of 360 monthly payments because as was

mentioned before there's 360 months in

30 years so the total amount that she's

gonna pay it's gonna be the monthly

payment times the number of payments

that she's gonna make so 1610 point 46

times 360

so that's five hundred seventy nine

thousand seven hundred sixty-five and

sixty cents so that's gonna be the total

amount of money that she's going to pay

now granted this isn't based on our

rounded answer if we want to find the

exact value we could take this number

and multiply it by 360 let's do that so

the exact value is five hundred seventy

nine thousand seven hundred sixty seven

dollars and thirty-five cents so we can

see the difference is approximately two

dollars so not too much of a difference

but nevertheless we can go from a

rounded answer because when you make a

monthly payment it's gonna be rounded

typically its rounded to the nearest

cent so this will be a reasonable answer

for Part B so now let's move on to Part

C calculate the total interest that she

will pay for this loan Sakhalin diya how

can we calculate the total interest the

total interest paid on this loan over a

time period of thirty years it's gonna

be the difference between the total

amount of money that she pays minus the

principal so we need to subtract this

number by three hundred thousand so all

I need to do is subtract five by three

and you'll get two hundred seventy nine

thousand seven hundred sixty-five

dollars and sixty cents so that's gonna

be the total amount of money that she's

going to pay in interest over a period

of 30 years now you might be wondering

that's a lot of money to pay an interest

but what are some ways in which she can

reduce the total interest that she's

going to pay over the lifetime of this

loan well there's two things that she

could do to reduce the total interest

paid

number one is to reduce the time period

of the loan if she can reduce the length

of the loan the total interest paid will

be reduced because there's less time for

interest to accumulate and the only way

to decrease the time period of the loan

is to make larger monthly payments if

she can increase her monthly payments

she's gonna pay off the loan a lot

faster so that's one way is you increase

your monthly payments that's going to

decrease the length of the loan and so

because you pay off the loan faster

interest has less time to accumulate on

your account balance and so the total

interest paid will be reduced so that's

number one pay off the loan faster by

increase in your monthly payment number

two is negotiate the second thing you

could do is reduce the interest rate on

the mortgage if you could bring down the

interest rate where all else is let's

say if everything else is the same

just by reducing the interest rate you

can reduce the total amount of interest

that you're gonna pay over the time

period of this loan so those are the two

ways you can bring down the interest

number one pay off the loan faster by

increasing your monthly payments or

number two negotiate for a better

interest rate so that's it for this

video now you know how to calculate the

monthly mortgage payment and also how to

calculate the total interest that you'll

pay on the loan given its given the time

period of the loan by the way for those

of you who want to get these answers in

Excel I've created a video titled how to

calculate the loan payment using the PMT

function in excel if you type it into

YouTube and then type in organic

chemistry tutor it's gonna show up but

I'm gonna also post a link in the

description section below so you can

just click on that link and find the

video that you're looking for and there

so feel free to take a look at that when

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