[Music] okay here I'm going to show two different amortization schedules for a loan so let's first look at what are the parameters of our loan here we've got four equal payments and we receive them at the end of each of the next four years so we got a total of four ,000 worth of payments so we discount those payments back to their uh present value here and using a 10% interest rate in this case and I got $3,170 for those annuity payments that we received at the end of each of the next four years now this $3,170 their uh present value here uh is our principal amount of this loan that represents the principle now if we look at the total payments here of $4,000 let their present value here of $3,170 the difference here is $830 and that's the interest that we have to amortise over the life of that loan either as a uh interest payable or an interest receivable so let's look at our first method here for our advertising this loan so we start out with a beginning balance here of $3,170 then we add in our interest expense or revenue for the year and then that would be 10% times the 31 uh $3,170 or $317 worth of interest for the year next we subtract out that payment that's made at the end of each year in this case it's $11,000 now subtracting that from the 3170 plus the 3117 gives us an ending balance here here of 30 $2,487 so the ending balance of year one becomes B beginning balance a year two and then we um determine our interest here by taking 10% our interest rate times the beginning balance here and we get an interest expense or or U expense or Revenue here add those two together less the payment give us gives us the ending balance of year two which becomes our beginning balance of year three now what this schedule uh 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 Ed here in this payment amount but to determine that you have to subtract out the interest so if you would subtract uh the interest each year from this payment amount you would be showing the principal now um that's that's something you have to look for if they're quizzing you on a problem and you have to have 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 uh um balance the beginning balance is the same $3,170 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 uh a 10% interest rate times your beginning balance there of 3170 and you get $317 worth of Interest here now you subtract this interest of $317 from the payment amount and you get uh 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 uh principle is based on the uh payment amount less the interest now that this here shows uh the principal reduction directly and it's a little bit more intuitive and a little bit easier to understand when you're advertising a loan so you have to be careful when you're solving your problems uh they may quiz you uh giving you one amount and then you have to be able to determine what is in it for example here you're given the payment amount up here and then your interest amount you have to understand that this payment includes the um 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 the these uh schedules and be able to understand how you calculate the interest and the principle in each one of these uh schedules