# Calculate remaining balance on a mortgage

(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
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,
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.

### Paul Whisler

1. David Lippman

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.

2. Euan Gamble

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

3. Yasmine

That's unprofessional video

4. Vinita

Thanks for the clear explanation.