Hi, welcome to Finance for Non-Finance Professionals.

I'd like to work another example with using the discounted cash flow analysis

that we've been working on the last couple of videos.

This example is going to be about mortgages or

money that you borrow usually for real estate transactions.

Mortgage is very simple debt instrument and

you're going to borrow money today to purchase real estate.

What we're going to do as you make your mortgage payments,

which are usually the same payment every month or every quarter or every year.

Part of that payment is principal and part of that payment is interest rate.

The way those two sort of hang together, how much is interest and

how much is principal is what we call an amortization schedule.

In this example, we're going to work a very simple mortgage together and

figure out how much the principal and

how much is interest in the amortization schedule or mortgage.

So, here's the simple example.

Let say, a bank charges you 7% interest per year.

You're going to borrow $10,000 and you're going to repay that $10,000

loan in three equal yearly installment of $3,810.52 over three years.

What we're going to do together is amortize the loan and

we're going to schedule out with the compound interest and

principle payment are on the mortgage.

What I've got worked for you here is a very simply amortization schedule.

In year zero, what you're borrowing right now is an amount of $10,000.

So, there's the 10,000.

That's your balance at the end of year zero, which is basically right now.

Right now, you've got a balance of 10,000.

What we're going to do is we're going to repay the loan in three payments of 3,810.

There's first payment, the second payment and the third payment.

So three payments, just like you make a regular mortgage payment.

On this example,

you're going to make a regular mortgage payment every year same amount a 3,810.

How much of that first payment is interest versus principal?

Well, if you got a balances outstanding of 10,000 and the interest rate is 7%.

What is 7% of 10,000?

That one easy, that just $700.

And so, your first payment of 38,10 includes a $700 interest repayment.

The rest of that amount, the rest of that 38,10 must be the principal payment.

So if I take that 38,10 and I subtract the 700, what do I have leftover?

I have $3,110.52.

That's how much principal I repaid.

So the 700 plus the 3110,

those 2 things together make 3,810.52.

So, I paid back 700 in interest and paid back 3110 in principal.

I take that 10,000 initial balance, subtract off how much principal I repaid.

I repaid 3,110 and that leaves me with a principal

balance at the end of the first year of $6,889.

That's how much balance I have left in principal.

The second payment of 3,810.52, how much of that is interest?

It's again, it's going to be 7% times how much principal I have left outstanding.

How much principle do I have left outstanding at the end of year one?

6,889, 7% of that is $482.86.

So in my second payment, there's less interest and more principal.

3,810 minus 482, get's me a principal payment of $3328.

So in the second payment, I've paid off a little less interest and

a little more principal.

That mean may remaining balance is now $6,889

minus the 3,328 in principal I repaid for

a total balance of 3,561.

At the end of 2 years after making payments of 3,810,

I'm left with a principle balanced of 3,561.

Now my third payment at the end of my third year, my third payment again,

my payment is always the same 3,810.

How much of that is interest?

Well, it's 7% of whatever my remaining balance was.

My remaining balance was the 3,561.

How much of that is paying paid an interest in the third year?

7% of that is 249.29.

3,810 minus 249 gives me how much principle I'm repaying, 3,561.22.

By magic and it's not really magic, that's the same amount of my balance.

Yeah, so these two things are equal.

Meaning that in my last payment of the amortization schedule, the remaining

principal pays off the remainder of the loan to give me an ending balance of zero.

All we did in this very simple amortization schedule for

a mortgage was apply the discounted cash flows of present valuing and

future valuing cash flows of compounding, and discounting,

and all we got from this was the full amortization schedule for any mortgage.

All of you now could go out and be loan officers at a commercial bank figuring out

amortization schedules based on these very simple principles of compounding and

discounting.