# FIN500 Mod03 P2 Loan Amortization For Principal And Interest Described Thru Amortization Schedule

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♪ Music playing in background ♪ Text on screen: Loan Amortization (Interest & Principal Schedules) Calculation Methods
Okay hearing gonna show two different amortization schedules for a loan,
so, let's first look at what our parameters of our loan.
Here we've got 4 equal payments, and we receive them at the in the end of each of the next 4 years.
So we got a total four thousand dollars worth of payments. So
we discount those payments back to their a present value here
and using a 10% interest rate in this case and I got
$3,170 dollars for those annuity payments that will be received at
the end of each of the next 4 years.
Now this $3,170 dollars there at present value here
is our principal amount of this loan.
That represents the principal. Now if we look at the total payments here of $4,000 dollars,
less there present value here of $3,170 dollars,
the difference here is $830 dollars.
And that's the interest that we have to amortize over to life for that loan
either as an interest payable or an interest receivable.
So let's look at our first method here for our amortizing this loan.
So we start out with the beginning balance here of
$3,170 dollars, then we add in our interest
expense or revenue for the year, and that would be
10% times $3,170 dollars
are $317 dollars interest for the year.
Next we subtract out that payment that's made at the end the each year
in this case it's $1,000 dollars.
Now subtracting that from the $3,170 plus the $317 gives
us an ending balance here your of $2,487 dollars.
So the ending balance of year one becomes the beginning balance of year two.
And then we determine our interest here by taking 10%
our interest rate times the beginning balance here, and we get an
interest expense or revenue here.
Add those two together less the payment gives us
the ending balance year two, which becomes our beginning balance of year three.
Now what this schedule up isn't showing you directly
is the principal reduction on the loan; that's the amount that this
ending balance is being reduced by each year. Now that principal reduction is included
here in this payment amount but to determine that
you have to subtract out the interest. So you would subtract
the interest each year from this a payment amount,
you would be shown the principal.
That's something you have to look for if they're quizzing you on a problem
and you have to have a pretty good understanding what's going on in here.
Now looking at this next schedule, it's a little bit more intuitive
where you begin your balance, the beginning balance, it's the same $3,170 dollars
and then you have your payment amount here,
now this payment amount, again, includes both the interest
and the principal amount. So you determine your interest in the same fashion
that would be a 10% interest rate times your beginning balance
there of $3,170, and you get $317 dollars worth of interest here.
Now you subtract this interest of $317 dollars from the payment and you get
your principal amount. That's the amount that the loan is being reduced by each period.
So here you've got your interest calculated
and your principle is
based on the payment amount less the interest.
Now this here shows the principal,
the reduction directly and it's a little bit more intuitive and a little
bit easier to understand when you're amortizing a loan.
So you have to be careful when you're
solving your problems; they may quiz you on
giving you 1 amount and then you have to be able to determine
what is in it. For example, here
given the payment amount up here, and then you interest amount
you have to understand that this is payment
includes the principal amount so you'd have
to subtract the interest from the payment to determine the principal.
Here it's done more directly here it's a little easier to understand.
So be aware of both of these schedules and be able to
understand how you calculate the interest
and the principal in each one of these schedules.