(male narrator)

So a couple purchases a home

with a $180,000 mortgage at a 4% rate for 30 years

with monthly payments. Uh…what will

the remaining balance in our mortgage be

after 5 years? Now to answer this, we’re gonna have

to do it in two parts. First thing we’re

gonna have to do is figure out what are

their monthly payments? Uh…so for that, we know that

our interest rate is 4%. We know we’re doing

monthly payments, uh…based on a 30-year

repayment schedule, uh…with an initial amount

of $180,000, and we’re looking

for d–our payment amount. So we pull out our loan formula,

and we set it up. So 1 plus .04, divided by 12

to the negative 12, times 30…

all over .04 over 12. Uh…and since we’ve done

a lot of these, I’m gonna go ahead and skip,

uh…a bunch of steps here. So I pull out my calculator,

and I calculate all of that. It comes out to be

about 209, uh…562, uh…and then divide

by that gives me a payment

of about $858.93. So the monthly payments

on this loan will be $858.93. So now that takes us to the

second part of the question. Now we know

the monthly payments, we can determine

the remaining balance. So we’re trying to find

the balance after 5 years. So after 5 years, there are 25 years left

to pay on the loan. So what we’re

really asking is how much loan balance

can be paid off in 25 years with monthly payments

of this size? In other words, keeping the interest rate

the same, if we have a loan for 25 years

with payments of $858.93, what is the loan balance at the beginning

of those 25 years? That is the current balance

of the loan after 5 years. So our P0 here,

where 0 now… times 0’s now 5 years in,

will be… uh…let’s see,

$858.93 is my d, times 1, minus 1,

plus .04 over 12, to the negative 12,

times 25– because remember we’re going

for 25 years now– over .04 over 12, and again, skipping

several steps here, uh…we come up

with 155,793, uh…91. So in other words,

after 5 years, uh…the remaining balance

on the loan will be 155,793. Now it’s worth thinking

about this number a little bit. So think about how much money

have we paid, uh…so far? So we’ve paid,

uh…$858.93 for 5 years, 12 times a year,

gives us a total of, uh… let’s see…51,535.80

that we’ve paid, uh…to the loan company,

right? That we’ve made

in payments. Uh…how much of the loan

have we actually paid off? Well, we started

with a $183,000 loan. After 5 years, our loan balance

is now 155,793, which means

we’ve paid off, uh…$24,206.09,

uh…paid off of the loan. Well, if we’ve paid

$51,535.80 and only $24,206.09 of it

has gone to the loan, then the other 27,329.71 must have gone

to interest so far. And of course,

the next 25 years, we’ll be adding

more interest, but over those

first 5 years, uh…we’ve paid

$27,000 in interest.

At 2:47, the value for P0 is incorrect. It should have been about $162,758. This would mean the couple has paid off about $17242 of the loan balance, and about $34,293 of what they have paid so far has been interest.

Thank you very much. I was quite stuck on this until you explained it.

That's unprofessional video

Thanks for the clear explanation.