[MUSIC] In part two of this lecture segment, we're going to jump into the topic of loan amortization and all loan amortization refers to is the schedule of payments that the borrower is agreeing to make to the lender to pay off that principle balance that they borrowed. So, loan amortization scheduling is just going to do layout, exactly when payments are due so that the borrower's going to pay that loan off over the agreed upon term. We're going to focus on fixed interest rates loans just because they have a very simple, or relatively simple amortization schedule. In a fixed interest rate loan the interest rate does not change. And we can find a payment level that's going to remain constant or fixed over the entire term length of the loan. So based on the term length, the interest rate and then how many payments are being made per year or the payment frequency on that loan given any certain amount that we might borrow we can figure out what that regular payment's going to be so that we pay off that loan over exactly the time period. That's defined by the term of the loan. So here we can see the formula that's used to determine the payment size for any given loan amortization schedule. So some of the basic terms that we discussed in the previous section are going to go into this formula. So the amount that we borrow or the initial principal balance the interest rate that's being charged on the loan on an annual basis, the term length of the loan, so again, the number of years over which we're going to be paying this loan back. And then finally, the payment frequency. So how many payments per year are we going to make? In terms of relating those to the different variables that go into the formula that you see on the screen here P is what we're finding. And that refers to the payment that's going to be made by the borrower during each payment period. Again, that can be on a monthly basis, an annual basis. That's defined by the payment frequency that's outlined in the loan contract. And then the values that you see within the formula itself that determine that payment V0 represents the initial principle balance, that's the amount that was originally borrowed, we have the annual interest rate of r, that is being charged on the loan, we have t, which defines the term length of the loan in years and then finally m, also enters in this formula, and that simply represents the number of payments that are going to be made during the year. On an annual payment frequency loan, m would be equal to one. On a monthly payment frequency loan, we would enter a value of 12 for m. You can see here that we take that annual interest rate and divide that by the number of payment periods throughout the year. What that gives us is the interest rate that's being charge per payment period. So for example if we're being charged 6% on annual basis or being charged roughly one half of a percentage point per month when we make those monthly loan payments. If we multiply the length of time we're paying the loan back in years t times m or the number payment periods per year T times M gives us the total number of payments that will be made. So again just as an example if we're talking about a 30 year home mortgage loan where we're making monthly payments, T would be equal to 30, M would be equal to 12, and the borrower would be agreeing to make a total of 360 payments if they're paying that agreed upon minimum to pay the loan off or pay that balance down to exactly zero over that 30 year period. Now, to just put some numbers into that formula to see what an example looks like. Let's assume that we're talking about a mortgage loan where we're borrowing $100,000. So, our value of V0 or our initial principal balance is 100,000. Let's look at a 6% annual interest rate, a term rate of 30 years. And a monthly payment frequency. If we enter these values into that loan amortization formula that we saw on the previous screen what that gives us is a monthly loan payment of $599.59 per month. What that tells us is that every month over the next 30 years or for the next 360 months The borrower will be required to pay a minimum of $599.55 back to the lender. If we make all $360 of those $599.55 payments, we'll pay off the loan balance, bring that loan balance down to 0 over that 30-year time frame. Here you can see what the loan amortization schedule looks like over the first year of this loan contract. Again, we're going to start with an initial loan balance of $100,000 in month 1, we'll make our first loan payment of $599.55 $500 of that or one half of percentage point on the $100,000 that we owe is going to be an interest payment. The remaining $99.55 is going to pay down our principle. That brings our principle balance down to $99,900.45 after that first month's loan payment. As we progress throughout the year, we can see that our loan payment remains the same. The amount of interest that we're being charged is declining because our principle balance is coming down as we make those loan payments and the portion that's going to payoff that principle continually increases throughout the payment schedule, throughout the life of this loan. If we move and take a look at the last year of what the amortization schedule would look like for this loans. So the final 12 payments in this 360 payments series. We can see by the 360th payment for still paying the $599.55 monthly payment. But that very last payment includes $2.98 worth of interest. And $596.57 worth of principle. [MUSIC] >> [NOISE]