Interest Calculation Methods 5210

Personal Finance presentation, interest calculation methods prepare to get financially fit by practicing personal finance, interest calculation methods, these will just be broad categories of general interest calculation methods given us concepts that we want to be keeping in mind when we’re thinking about financing, when we’re thinking about loan options, they make a lot more sense when we work practice problems, and we get the concepts down much better.


By doing so we will be working in many practice problems in both Excel and presentation format, highly recommend taking a look at those for more detail. So we’ll list out the methods we’ll take a look at here. And then we’ll go into each of them in more detail, the starting point will typically be the simple interest, the simple interest is kind of a building block of other type of of interest kind of formats, it could be set up in the loan, then we’ve got the simple interest on declining balance, which is often a concept that will be related to the typical type of loans that are over a year long installment type loans,



then we’ve got add on interest, this is something that could be applied, and it’s not as common, but some loans could be set up in this way. And if that’s the case, you want to be aware of it and think about how that interest is calculated there as well. So typically, whenever thinking about interest, we’re thinking about, in essence, the rent on the purchasing power of the money for taking out a loan, we are getting, in essence rented the purchasing power, and they’re going to be charging us for the use of it over time as we use the purchasing power of it overtime, kind of like rent.



But that’s going to be what the interest calculation is, then, of course, how are we going to calculate interest, the simple interest is kind of the starting point, the building blocks that we need to understand when we then move on to, you know, other types of interest type of calculations. So it’s going to be computed on principal only without compounding the dollar cost of borrowing. And it’s calculated as simply the interest equaling the principal loan balance the principal times the rate at times the time, so principal times rate times time, P times R times T, you might see, so obviously, the principal represents the loan, in essence, that’s going to be outstanding.



If we say the principal, for example, is 1000, then we’re gonna say that’s the principal the rate. Normally, when we think about rates unless they say otherwise, the rate is going to be generally a yearly rate. So if we were taking, if we were saying $1,000, with a yearly rate of 5%, that would be times point, oh five, and then we would have and that would be 50. And then if we if that was a yearly type of calculation, times one year, in this case, we’d say times one would be the time of one, and then we’ve got the 50 calculation here. Now, if you were to, if you wanted to break this down to like a monthly, you got to make sure that you’re matching out the rate.



And the timeframe that’s going to be that’s going to be taking place. So for example, if you’re taking a interest rate, that’s going to be a monthly rate, which let’s say like 1%, so to take like 12%, for a year, if there was a 12% yearly rate, divided by 12, then we’d have a monthly rate of 1%. If we took that times the principal times the principal of 1000, that’s going to be $10, on a monthly rate basis, and then you times the time, the time here needs to be matching the same periods as the rate in essence, right. So if you’re saying it’s a five month type of situation, then we’re gonna say times five. And then we just have a simple interest calculation of 50. Over the five month time frame, notice, once again, we didn’t have any compound in that is taking place there.



So it’s just a simple interest calculation, the principal times the rate times the time, just making sure that the rate and the time hour are matching up for the simple interest calculation. Now most of the time, when you set up the loan, you’re going to be setting up in that installment type of loan setup. So usually, it’s going to be a loan that can be longer than a year long, the calculation we’re thinking about is usually going to be simple interest on a declining type of balance situation. And that’s what we want to get used to as kind of a standard even though that standard is a bit complex.



And so that’s where the interest is paid only on the amount of the original principle not yet repaid. Because what’s going to happen in this type of situation is we’re going to be paying back installments, which include a portion of the principal and a portion of the interest. When that is the case. If we have a reduction and the loan balance on a periodic basis, then we can have a reduction in the amount of interest that’s going to be calculated. So you’re using the similar kind of calculation for the interest,



but you’ve got this reducing kind of situation that’s going on. Let’s take input. So this actually gets us a little bit complicated, because in this situation, what we’re trying to do on the financing side is typically keep the payments the same, and then have the variance, that’s going to be changing between the allocation between the interest and principal. So that means in order to keep the payment the same, and have this declining kind of method that’s going to be used, the allocation between interest and, and the principal reduction is going to change with each payment.



So we got to get an idea of that the best way to get an idea of what is actually happening there is to do calculations in Excel Excel are very helpful to help us to build these kind of tables, and we get a much better sense of what’s going on. So in this case, for example, if you have the 12% interest, and we say that’s the yearly interest rate, and we put together our table, then, and we’ll let’s say this time, we took out a $100,000 loan, at time period zero, the payments are working out to be 2000 to 24.



Note that in the practice problems, we’ll see how to calculate the payments and how to figure out what the payments would be. So you can practice on that. But we’re concerned here with the interest payments. So if you made a payment of 2000 to 24. And we’re breaking out the interest portion of 1000. That 1000 being calculated here as the 100,000 times the yearly rate, which is point one to 12%, that would be 12,000 for a year. But this we’re assuming is a monthly payment, so we’re going to divide that by 12. That’s where we’re getting that 1000. So that means that if you paid 2224 minus 1000,



that there’s going to be a reduction in the principle of 1224. So that means the new principal balance at this point has declined 100,000 minus the one two to four about is the 98 776. So then we’re going to calculate on the next component, we’re still paying another 2000 to 24. But now that we’ve got this declined amount here, so we’re going to take that 98 776 and multiply it times the point one, two, that would give us the 11 853. If it was a yearly amount divided by 12. That’ll give us the 988.



About, you can also calculate that as we saw before, when we saw our simple interest calculation, if that’s the rate for a year, then you can break out the rate for a month, which would be point one, two divided by 12, the monthly rate would be point O one, or 1% 1% times the principal of 100,000 would be 1000 per month times the period times the number of periods, which in this case is one right times one month would be the 1000. That’s how we got to that 1000. The second one would be the 98776 times point oh one would be the MFI rate getting us right to that 988 here times one because it’s one month.



And then if we subtract this out, we have rounded involved, but it’s 2224 minus 2988, that would give us the 1237. And then if we take the 98776 minus 1237. About, we get about that 97539. So that’s going to be kind of a typical structure that we will be using, oftentimes loans will be set up in and you can see how we’re kind of very 18 from that typical normal simple interest type of calculation in order to apply it here, in order to set up these types of loans and understand what the payment will be very useful to be able to set up these amortization tables highly recommend going through the practice problems to get a better feel of these amortization tables, because they really give you a better understanding of what’s going on, then we have the add on interest.



This is actually an easier method to calculate in some ways, but it’s not really the standard type of installment loan that we typically see. So if you were to see a loan structure of this sort, then it’s a little bit more difficult to compare it to standard loan structure, even though it’s easier to calculate. And we do have some practice problems to help you to do that comparison.



So anytime there’s a variant from what you’re used to the standards here, then the question is, well, how can I standardize these things? So I’m comparing apples to apples. And when you look at something like an add on interest, and you compare that to like a normal installment loan, then your question is, well, what’s the differences? How much more you know, what’s the difference in terms of the rates that I’m paying, and so on.



So this is going to be interest calculated on the full amount of the principal interest added to the original principal, and then the payment equals the total divided by the number of payments to be made. Let’s take a look at a quick example. We do have an example of this on the practice problem as well so you can get a better idea of it. But let’s say that we had a loan for the 10,400. And we had a rate of the 8%. Now, the simple interest calculation would simply be the principal times the rate times the time. So if we took this case, we’d say simple interest calculation would be nice and simple, we’d say the 10,400 times point O eight yearly rate would be 832.



And I’m not going to compound it or anything, I’m just going to say that means I’m going to have that for the number of periods, which in this case is four years. So times time, times four. Notice, as we do this, this rate right here is a yearly rate. And this amount right here in terms of years is, in years, those two things, it has to be matching up, you got to be careful making sure that those match up, if you’re using months here,



then you should generally have a monthly rate, then we’re going to take then the interest over the full time period, the four years, add that to the to the loan amount of the 10,400, that then given us the total amount that we were going to pay over this thing 13,007 28. So we’re going to take that 13,007 28, and then try to pay it off periodically, meaning we’re going to take the number of years, which are four years, and then try to pay it off monthly, times 12. That’ll give us 48 payments.



So we’re gonna take the full amount already calculating just simply the in the simple interest, and then we’ll just say, okay, we’re gonna pay off the 13 728, over 48 months, or four years monthly payments, that would give us a payment each month of the 286. Now that’s, that’s kind of nice and easy to calculate. So but when I do a comparison between this type of calculation and the calculation on an installment calculation, it’s a bit confusing, because you can see, as we pay this off, we’re actually paying off, you know, part of the of the interest and part of the principal.



So although it’s, it’s kind of easy to calculate here, if I was, it’s hard to compare what the actual costs that I’m paying up to an installment loan, because this rate is basically on different terms, this is a simple interest rate. And we’re usually used to if we’re looking at installment loans, this kind of declining situation. So you do in order to compare those two, we have some practice problems to take a look at that.



It’s also a little confusing, just to kind of record this logistically, if you put this on the books and record the interest on like an accrual type of basis, you would think you’d put the loan on the books for the 10,400. And then you’d have to break out this payment between the the interest and principal. And if it was a, if it was like, like a generally accepted accounting principles business setting, I would assume that you would have to actually impute the interest and figure out the breakout. But if you just use this format, you could then say, Okay, well, then that means that that that ratio of say interest,



which is three, three to eight, divided by the total total amount of the 1378, would be that point 2424. So that means that if I take that 286 times 2.24, so times 286, each of each payment, we can assume has a principal portion of 69. And the difference, the and the rest of it being I’m sorry, it has an interest portion of 69. And the rest of it being the principal. So we could, we could record it that way fairly easily. So in other words, if I made 286 payments, and I assigned 69.333, to each one of them as interest, and I did that for 48 periods, we would get up to the total of the 3328 of interest.



So you can record it from a bookkeeping standpoint that way. And again, it’s actually easier, because you don’t have this variance or difference between interest in principle, you don’t need the amortization table to kind of record it, you can actually memorize the transaction and record a set amount. However, it’s not exactly the way you’re supposed to do it. Because you’re supposed to do that declining, you know, you’re supposed to only be calculating the interest on the balance, usually, and whatnot. So that compatibility is kind of the problem, this one is a little bit easier to calculate.



But it’s not what we typically think of when we do the comparison. So if you see a loan structured This way, you can’t compare this 8% interest to the same rates you might have on installment, it’ll typically be higher if I was to do that comparison. And we’ll see that in a practice problem to try to compare these two things out. So anytime again, if you see a variant from kind of a standard, and the standard is typically some kind of installment situation like this. On the standard loan setups, it’s going to be more difficult to compare your options from one to the other. And you’re going to look for ways to compare basically apples to apples. We’ll do that with some practice. Problems

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