FIN 25 Annuity Due

Well, let's have a look at problem three, 17, a it's called an annuity due. So an annuity, you make a payment at the end of each period, uh, for a certain number of years. And we calculate the present value of those payments using this formula for an annuity due. It's the exact same thing as the present value of an annuity, except for you don't pay at the end of the period. You pay at the start of the period. And as a consequence, you get one more year of interest accruing on this because you're paying at the start of the period. So you get one more period of interest accruing. So it's a simple matter of multiplying whatever the result there was by one plus the, uh, discount rate or the interest rate. And that's it. You, you're just sort of adding an extra year's worth of interest because you're contributing the money a year. So in any event, that's sort of the only difference between PV of an annuity and an annuity due annuity due. So let's solve your company finances, a new piece of equipment with a price of $250,000. The contract calls for monthly payments for the next 48 months. Starting today, it's an annuity due, uh, the interest rate is 11.5% APR calculate the monthly payment. Okay. So we're quoted an APR interest rate. So we've actually got a bit of work to do there and we're solving here for C right. We're solving here for the payment amount. So let's start by figuring out the, uh, interest rate on a monthly basis, because again, we're looking at this thing, uh, monthly payments. So we want to figure out the C per month, right? The payment, the cashflow per month. So it's an 11.5% annualized rate, APR to figure out the monthly, you actually just, it's very simple with APR. You just divide by 12. So 0.115 divided by 12 equals a little bit awkward for our calculator 0.00958333, right? So it's 0.95% or 0.96%. We'll leave it as 0.00958333, because that's, what's going to go into our calculator. Okay. So let's punch in the numbers. We know, we actually know the value of the annuity. It's got to be 250,000 bucks. It's the price of the equipment. So two 50, maybe I'll write this underneath two 50 is our PV of our annuity equals C. That's what we're solving for times. And then big awkward brackets, uh, we'll deal with that in a second. So times one minus one over one plus R, which is this 0.0095833. So 1.0095833 to the power of T 48 payments, 48 months. So to the power of 48, and we divide that by 0.00958333. You take as many decimal places as you reasonably can. And then we're going to multiply that by 1.0095833. Okay. There we have it. We've got the formula. Now it's just a matter of like working with our calculator. Uh, so I'm going to add one here. Oops, I right-clicked add one to get 1.0095833. I'm going to raise that to the power of 48 to the 48th power Y to the X 48. So now I got this, uh, exponent dealt with. I go one over X. So one divided by that amount is 0.63, one minus that amount. So minus one plus minus. So one minus 0.63 is 0.36. Uh, divide by that magic number, divide by 0.0095833333. I get 38.33. So what's in the brackets is 38.33. I'm going to multiply that by 1.00958333. So let's do that now times 1.0095833333. I get 38.69765. So I have, let me just fill this rest of this out. C times that equals 250. Let's continue to work this down. 250 equals C times 38.69765, 38.698 we'll call it. Uh, so then 250 divided by 38 is going to be our answer. So I just go one over X times 250 and that gets us the same result. 6460.34 C equals 6460.34. We've solved it. So it's what's the monthly payment on this new piece of equipment. It's $6,460.34 per month. Well done. We've solved the problem. Um, let's crunch those numbers in our financial calculator. So, uh, N is 48. So 48 is N. IY is going to be this 0.0095833, but remember we put in the percentage. So if it was 8%, I don't put 0.08 in my calculator. I would just put the number eight. So here it's actually 0.958333%. That's the number that goes into my calculator. I gotta be careful there. It can be a little confusing, but that's the number that needs to go in. 0.95833333. That's my IY. Uh, my PV, we actually know is 250,000 positive PV. We don't know our payment. Our FV is going to be zero. And now we're going to compute a payment. So, oh, I almost did it. I almost did it. I'm clearing. Uh, I forgot to put on begin. Of course, this is an annuity due. I, that's a key step here, right? Uh, cause otherwise we would have just been computing this without this little feature on the end. So I have to tell my calculator, this is an annuity due. So to get it to do that, I go second function begin. I go second function set, and then I clear. So I think all my numbers are still in there. I'm going to compute PMT. That's what we're looking for. And there it is. I got the right number, right? 6460.34. I'm feeling pretty good about myself. I hope you're feeling pretty good about yourself. When you leave a problem like this, make sure you switch the begin back off. So I go second function begin, second function set, clear. Right now, my calculator is back to normal, but you saw, we did it in the financial calculator. We've also done it by hand. We've solved 317A. As always, hope the video helped. Bye for now.