Compound Interest – Mortgages Welcome to another BA II Calculator series
on compound interest, and today we are going to look at mortgages. Well, quite simply a mortgage, is we are buying
a house and we have to pay off the loan of the mortgage, and this is how we are going
to do it. With mortgages we can either compute the N
for number of payments, or the PMT for the payment size itself. Just depends on what the question is asking
us. Once we have done that, depending on how long
the term is supposed to last, we might have to do a second calculation to figure out the
payments for the next term of our mortgage. So, we will use the amortization function
to figure out how much is left owing on the mortgage after the first term is done. Okay, you have just purchased a house that
has a mortgage of $200,000. You are going to be making payments at the
end of each month for the whole 25 year mortgage period.
If the interest rate is 4.9% per month for
the first 5 years, how much would your monthly payments be? So, at the bottom of the question here, the
question is asking how much are you monthly payments, so how much is PMT? Let’s go back to the top and start working
our way through the question and start picking out the information we need. So, first thing we talk about is the mortgage
itself, so we have a mortgage of $200,000. Mortgage is like a loan, so this is another
word for PV. So 200,000 here , this is PV. You are going to be making the payments at
the end of each month, so the end of each month. So your calculator needs to be in end mode,
which it should always be set in end mode unless you switch it to begin. You can watch a video how to switch your calculator
to begin to end mode, and how to switch back from begin mode to end mode. Our payments begin at the end of the month
so this is our PY, for the whole 25 year mortgage. So we are going to use the 25 for RN.
If the interest rate is 4.9% per month, s
our IY, for the first 5 years, so you can see this interest rate is only going to be
for 5 years, however the whole 25 year term. So that means we will have to do a second
question where the interest rate will be different for the next 5 years. Okay, let’s set up our row of buttons. So the first thing is our mortgage is 200,000,
so that’s our present value. You are going to be making payments at the
end, and my calculator is already in end mode.
Each month, so PY is 12, for the whole 25
years, so even though this interest rate is 4.9% for the first five years, the mortgage
itself is for 25 year term. So 25 years times the 12 is 300. This is how many payments we are going to
be making over the whole life of the mortgage. And, so when you calculate N, N has to be
based on the total life of the mortgage, not just how many years the first interest rate
is going to be. The interest rate is 4.9, we are looking for
payments, future value is going to be zero, and the compounding is per month.
So CY is per month. Okay, so let’s turn the calculator on, so
300 N, 4.9 IY, 200,000 PV, zero FV, and we will go into our second function IY, I have
set my calculator to PY as 12 and if I scroll down my CY is also 12, and remember, if it
is not 12 already, enter 12. And then down. And then we go 2nd quite to get out, and then
we go CPT PMT, so compute payment, so our mortgage is going to be $1157.56 per month
for the first five years. I know we used 300 as payment, but these are
our payments for the first 5 years because our interest rate is 4.9% at this time.
Now, in the second question, it says: if you
had renewed your mortgage at 5.1% per month for the next 5 years how much would your payments
be now? So what we want to do is we need to figure
out the present value after we just finished doing the first 5 years of payments at the
original amount that we just calculated here in our calculator at $1157.57. so to do that we are going to go back into
our amortization function, so we are going to go 2nd amort, 2nd PV, and in this function
we now have to figure out how many payments we are going to make in those 5 years. So that 5 years, and the payments were once
a month, or 12 times a year, so we would make 60 payments total.
So, that means for P1 we want to set 60, and
P2 we want to set 60, and then we want to scroll to the balance. If you can’t remember how to use your amortization
function you can watch the video on the amortization function. So I am going to go 60 and 60 and scroll to
my balance. And again it just takes a few seconds for
the calculator to compute that, and I get $176, 876.42. This balance will become our present value
in our next calculation. So let’s just go back to the top of the
question, read through it and pull the information out.
The first thing we have here is this 5.1 this
is going to be our new IY, again it’s per month so CY will remain 12. Now I know it says for the next 5 years, the
mortgage was 25 years in total. So when it comes time to doing my N, what
we need to do is subtract and figure out how many payments are actually left in the 25
year period. So, we started with 25 years in total, we
just finished the first 5, so there are 20 years remaining. We are going to make a payment once a month
for 12 times a year so there are 240 payments remaining for our N. Let’s just get out
of this, so go 2nd quit, so there is our N, 240 N, the IY is the 5.1, the PV is now the
$176,876.42, and I am just going to make sure there is zero FV, payment is what we are looking
for. PY and CY are going to remain at 12 each. We should check to make sure they are 12 and
12. 2nd quit, and the CPT PMT. And our new payments are $1177.10.
Now this is just the size of our new payments,
we are not quite done yet because the question says: how much would your monthly payments
be now. We are done. Ok, we’re done. These are our new payments. $1177.10. This has been another presentation of the
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