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PROFESSOR: All right.
Hopefully you've looked at the solutions A for problems 7.1
through 7.3, and you got comfortable using the tables.
And now we're going to start looking at how we use these
tables to calculate loans and amortization tables, and
things like that.
What 7.6 is, is it's an assumption that you've bought
a pizza oven.
You've borrowed $15,000 at 12% for four years, and we need to
calculate the payment on this.
Of course, the payments are four equal payments, and what
we do is we take the formula payment equals loan amount
divided by PVA.
The loan amount was $15,000, and the PVA was for four years
at 12%, so we go to the PVA table, we go to four years at
12%, we see 3.0373.
We do the math, I don't know why I have two dollar signs
there, we have $4,938.
So our loan amount as $4,938 on this problem.
On 7.7, what we need to do is we need to go ahead and
develop an amortization table.
And there is an example of an amortization table.
I should have it right in front of me, but I don't.
[INAUDIBLE] closer.
Where it that example?
On 214 of your text, and there was one also in the lecture
for chapter seven.
So we need to go ahead and calculate the payment before
we can do an amortization table.
And this loan was for $6,000, the interest was 10%, and it
was in three equal installments, so it was for
three years.
So we take our payment, divide it by loan amount, where
payment equals loan amount divided by PVA, and we get
$24,126 as the payment on the loan.
Then we need to develop an amortization table.
I didn't know the best way to do this kind of problem, so I
put the amortization table up here completed, and we'll just
walk through it.
The first thing you can do is just put your payments down.
So what you should have on here is you should have on
time period zero, you've got a balance of $6,000.
We know that because that's the loan, and then we just
calculate our payments.
So you can go down, you can put $24,126.89 down.
And then we have to fill in the interest, the principal,
and the remaining balance to get to approximately zero.
OK, so assuming that you've put $6,000 for your balance,
and now we've calculated our payments, and we've put the
$24,126.89 down three times for years one through three,
we need to calculate interest.
This loan is for 10%, so we take 0.10, multiply it by
$60,000, and we get 6,000.
If you remember right, the payment is made up of two
things, interest and principal.
So we take the $24,126.89, we subtract our interest of
$6,000, and we get the principal of $18,126.89.
Now, principal reduces our balance, so we subtract the
$60,000 by our principle.
$60,000 minus $18,126.89 is $41,873.11.
So again, to review, the interest is the interest rate
multiplied by the balance.
The principal and the interest equal the payment, and the
balance is reduced by the principal.
So on your two, you should see your interest decline because
your balance declined.
So on year two, what we did is we multiplied 10% by our
balance, which is $41,873, and we get $4,187.31.
We subtract that from our payment to find our principal,
because our interest plus principal equals payment.
We get $19,939.58.
Now, again, as our interest goes down, our
principle goes up.
And we take our principle for year two, we subtract it from
the balance of year one, and we get $21,933.53.
For our final year, we need to go ahead and calculate the
interest once again, and that's 10% of our new balance,
so we get $2,193.35, and we subtract
that from our payment.
We get $21,933.54, and we subtract
that from our balance.
We get a penny.
We are actually off a penny.
Your balance for your final year could
be $10 or $12 there.
It's all rounding, and it all just depends on how you're
plugging your numbers into your calculator, but it's
never going to be zero.
And if any of you all ever have a loan, your last payment
is actually a couple dollars more or less than your other
payments, and that's because of rounding.
So this is one of those concepts, and I say this over
and over again, that you have to practice it four, five, six
times to get it right.
I would actually go ahead and go to 7.6 and calculate an
amortization table.
And if you do so and you want me to look at it, you can
email it to me, and I'll let you know if
it's correct or not.
I believe we have an amortizaiton table or two in
the study guide, also.
You need to work these number of times, so that when you
have a problem like this on the test, it's second nature.
If it's not second nature, you're going to bomb it.
And this is one of those deals where you're not just going to
go ahead and get a couple numbers off, you're just going
to freeze up, and you're going to get a zero.
And I don't want anybody to get a zero, so work these and
understand these.
And if you just can't figure it out, you need to call me,
and we'll talk through it, and I'll talk you through the
calculations.
And we may even work on new problems so that you can see
how it flows, and you're not staring at the solution where
you're trying to work the problem.
All right, so now we have one more homework solution, and
that's the study guide, and will be doing that shortly.