 Personal finance practice problem using one note, coupon savings calculation. Prepare to get financially fit by practicing personal finance. If you have access to one note, would like to follow along when the icon on the left hand side practice problems tab in the 6170 coupon savings calculation tab. Also note that you might wanna take a look at the immersive reader tool and the text files which should have the same name and number and possibly the transcripts that can be translated into multiple languages and either listened to or read in them. We're gonna be using our time value of money calculations, our present value and future value calculations to think about the savings over time we might get from the use of coupons. As we do so, wanna keep a couple things in mind. One would be how someone might use present value and future calculations in order to basically make an argument and support their argument. So for example here, if you're talking to someone that's trying to give you or tell you about the value of the use of coupons over time, what type of calculations might they use from present value and future value calculations to support their argument? If you were talking to someone that's trying to say that coupons aren't worthwhile, they're not saving you as much money as you think and the time is not worth the savings, what kind of present value and future value arguments might they use or how might they frame the argument? And then of course, if you were trying to make a decision yourself in terms of what kind of habits do I want to be putting in place with regards to things like saving coupons, then how can I compile my data so that I can make a fair decision? So remember that the present value and future calculations are usually there for longer term type of decisions because that's when we wanna make a more systematic decision making process. When we're talking about habits such as the use of coupons for example, then we wanna possibly look at it in a long-term kind of perspective and then try to gear our day-to-day behavior to basically be in alignment with what we think is good for that long-term perspective, not doing this calculation every time we buy a coupon for example, but if we've come to the conclusion that doing coupons is worthwhile for us, then getting into habit and trusting that long-term calculation we've made to do them or vice versa, right? So these are the general ideas we wanna keep in mind. So we're gonna assume the savings due to coupons each month are gonna be $75. So the amount saved after years of six years at a rate of 8%. So if you saved $75 with the use of coupons then after six years, what would your savings be or what would be your future value be if you were able to get an 8% return on that $75. So we could say, okay, well that would mean we'd have the monthly savings of $75. The quick calculation would be that after a year we would say 75 times 12, that would give us then $900 after a year that we would save with the use of coupons. So now of course, we could do that quick calculation and kind of compare and contrast the $900 versus the time that we put in to save the $75 a month for the coupons and that's the first kind of thought process or calculation we might try to annualize in that way. Then we could say, okay, let's try to take the easiest kind of future value calculation using that $900. If I was to save $900 for a year by using the coupons, then I could say, let's do a future value calculation and see how much we would have in future value terms after the six year timeframe. So if you did this in Excel I won't go into this in detail. We did do this in Excel but it would be a future value calculation looking like this. You could also do it with a calculator. You could do it with tables. We won't get into all that but you'll use your future value tools which is the future value of the rate. So we're picking up the rate which is gonna be 8% per year. We're using a yearly rate because we annualized the savings of the coupons and then we've got the argument for the number of periods which we're gonna use six. We're talking years, not months. That's why we annualized it to kind of simplify the problem a bit because it's just an estimate and then comma and then we've got the payment amount which we're gonna say is $900. We're not actually putting $900 or saving $900 per year. We're actually saving 75 per month. So we're estimating it again to make it a yearly kind of calculation and that's what we have to do to simplify the calculation for the tool. We could also do it on a monthly basis. We might take a look at that as well but that would give us then future value of 6,602. Now note that if we were trying to argue from the standpoint that having in habit of saving coupons is a good idea, a good thing, then we would probably use a calculation like this because we end up with the future value. So we're gonna say, yeah, if you save 75 and you were able to put that away and earn the 8% then after the six years you might be at that 6,602 but that's kind of like a future value term number at the same time. So I just point this out because this happens a lot of times whenever you're talking about longer term types of projects and we're using these time value of money calculations, oftentimes when people are presenting these calculations they might have an interest in whatever the decision outcome will be and you wanna know what the interest is for the individual because it's likely they're gonna be gearing their calculations in the most optimistic type of way and looking at the calculations from one lens. And clearly what we want to do is from a fair decision standpoint is look at it from multiple lens and then make a decision after we've seen all the angles that are going to be involved in it. So just something you wanna just kind of keep in mind whenever these tools are gonna be used, whenever statistics are used in general, whenever words are used you have the same problem, right? People make arguments that are supporting and they leave out other arguments. We see that with word arguments, numbers are the same thing, right? You could present one side of the argument. Okay, so we could say, hey, yeah, but that's still kind of that's like future value numbers. You could kind of calculate a middle value number. You could say, well, maybe I'm not gonna earn the 8%. Maybe if I save $75, then I'm not gonna be able to get the 8%. So you could try to get a middle ground number and say, well, really I'm gonna get the 900 per year times six years. That would be the $5,400 that we would earn and you could go on a more, you know, the pessimistic side of things and say, well, yeah, I'm gonna save the $75, but I'm gonna have to put time in it and so on to do it as well. And I don't think I'm gonna earn the 8%. What I'm really gonna do is I'm gonna have this $900 that I'm gonna discount over the next six years and add a discount rate. We'll use the same 8% of the discount rate because if I'm saving, if you're telling me I'm saving $900 a year and I'm not earning say 8% on it, the first $900 and the first year is worth more than the second $900 the second year out. So you could say, well, if I did that for six years and I discounted back to the present value, in other words, what would this stream of $900 be if I was to receive $900 each year for the next six years, you could say, okay, well, if I take the present value of the rate and the rate is going to be, we're gonna use the same 8% here, the number of periods we're gonna say is the six years. So I got six years and the payment this time, we're gonna get the payment of the $900, a series of payments that we're going to be receiving, then if I discount that, that would be the most pessimistic number of the 4,161. So again, if you can see someone was making the arguments on this type of thing, if they had a stake or an interest in the outcome and they wanted this action to be taken, in this case, using the coupons, they'd probably use the most optimistic number, assuming we're getting a gain on it. And if you run the pessimistic side, you'd say, well, yeah, no, I'm not sure I'm gonna get that gain. In fact, I think I'm just gonna get the cash flow of the $600 or the $900 for the six years. And if I discount that at that rate that you're using, really the cash flow payments would be worth the 4,161. So the bottom line, I just wanna note that you wanna be able to look at things from multiple different angles with regards to saving money and of course, putting in habits that save money. I think that could clearly accumulate over time and be a useful thing to do. But like anything else, when you're kinda training yourself to have those habits, you wanna weigh out the pros and cons and take into consider the savings and the amount of time that's gonna be put into that savings as well. And also just the kind of changes in the purchasing habits that you might have if you're using coupons. Cause obviously then you're gonna be guided to purchase the products that are gonna have the coupons and so on and so forth and that kinda alters behavior in some instance as well. Now we could think about this a couple different ways. Let's just do our time value of money calculations. If I was gonna verify this calculation down below, I can do it this way. And we could say if we have periods, let's say we have periods one through six and we're starting off with the $900, this is how the calculation's going to work. So then we're gonna say that in period one, when we do an annuity calculation, we're not calculating any interest at that point. So you gotta keep in mind that starting point that we're gonna be working on and then we're gonna be calculating the savings on it. Assuming we invest the 900, so we've got the 900 times the 0.08, there's the 72 and then we're gonna add that to plus the 900 that we're gonna put in at the end of the second period plus the 900 we started with, there's the 1872. Then on that 1872, we're gonna say multiply that times the 0.08 and that's gonna give us the about 450 and we're gonna put in another 900 plus the 900 and we had the prior balance of the 1872, so that's gonna be the 2922 about and then let's do it one more time, we'll take that and multiply it to times the 0.08 and that's gonna give us our 234 about plus we're gonna put in the 900 again and we had the prior balance of the 2922 and there's the 4052, that then if we do that all the way down gets us to that 6602. So it's nice to be able to see how to get to that 6602 with an actual table that gives us a better idea. Also note that we did kind of estimate this because the 900 we're actually having savings per month and so when we do a periodic table that's on the end of each year then that's gonna be a type of simplification which may or may not be a problem because it's just an estimate so sometimes those simplifications are not a problem due to the fact that it's an estimate. Now if I was to basically present value that, let's just assume just to get an idea and say okay, well yeah, but that's in future value terms. So if I was to present value that number at the same discount rate just to show you how these present value and future values work, we could say okay, I'm gonna take that number, that 6602 and do a present value calculation at the rate of the 8% and then the number of periods is gonna be six and then the payment is going to be, and I'm not gonna take the payment, comma, comma, I'm gonna take the present value of that future value, the 4,000, I mean the 6602 that we came out to and that present value calculation would get us back to that 4,161 just so you could see how those two items are playing out. Now you could also do this on a month by month basis, you might say, hey look, that's kind of a, you know, you kind of rounded, why don't, if I'm saving 75 a month and I'm gonna put that into the bank and get savings on it each month, why don't I do the future value calculation on a monthly basis instead of annualizing it? You could do that. So you come up with a slightly different number so you can see how we kind of rounded it up here, come up with a slightly different here because if you took the $75 and put it into savings each month and earned the annual rate of 8%, it would look something like this, we'd say the future value, the rate now would be this number, the 8% divided by 12 because now we're talking on a month by month basis and then comma, the number of periods, now we're talking six years times 12 because we're on a month by month basis and then the payment would be not the 900 but the $75 each month and that gets to the 6902 and it's a little bit higher because now we're getting, we're earning not on just the 900 at the year total but on each month that we put the 75 in and we could do the same thing with the present value calculation. We could something a little bit different than we had up top, we could say well the present value of the rate which is gonna be the 8% divided by 12 to get the monthly rate, the number of periods would be these six years and then we multiply by 12 to get to the months and then we're gonna say that the payment now is not the 900 but the 75 and we would get the present value of the 4,278.