 Hello and welcome to the session in which we will discuss the third annuity. Before you learn about the third annuity, make sure you understand the present value of an ordinary annuity and a single payment and the future value of an ordinary annuity and the future value of a single payment. It's critical. Don't attempt the third annuity until unless you have the basics because without understanding those two you won't be able to understand the concept of the third annuity. Now this topic is covered usually in a finance course but you could see it also on the CPA exam in a multiple choice where you are being asked to find the present value of a third annuity. Whether you are an accounting student or a finance student or a CPA candidate for that matter, I strongly suggest you take a look at my website farhatlectures.com. I don't replace your CPA review course. I'm a useful addition. I explain the material differently than your CPA review course. I can help you understand your CPA review course better. Your subscription is one month. You can try me. See if you like it. You like it. You keep it. You don't. You cancel it. So your risk is limited to one month but your potential gain is passing the exam. My resources cover many other accounting courses such as intermediate, governmental, tax, events, so on and so forth. My supplemental review courses, my supplemental review courses are aligned with your actual review course whether it's Becker, Roger, Wiley or Gleam and I do have all the AI CPA previously previously released questions which is approximately 1500 of them with detailed solution. Please connect with me on social media if you haven't done so and connect with me on LinkedIn and take a look at my LinkedIn recommendation like this recording. Share it with other connect with me on Instagram, Facebook, Twitter and Reddit. So let's take a look at the deferred annuity and what does it mean? It means that the rent payments begins after a specified period in the future. So simply put it looks something like this. If this is the time frame, this is 0, 1, 2, 3. So the payments don't order seats don't start until year 4, year 5, year 6. So the first three years you don't get anything or you don't pay anything. So this is what a deferred annuity is. So we have to compute the deferred annuity whether it's the future value or the present value. The good thing about the future value, it's the same thing as the future value of a regular annuity. There's nothing to the third about. So if you are being asked to compute the future value of an amount that's starting in year 3, it goes from year 3, 4, 5 and 6, 3, 4, 5 and 6, it doesn't really matter. The future value is the same computation. You don't have to make any adjustment. The present value of the third annuity would require you to take two-step process. The step one is to find the present value of the annuity at the future date. So basically find the present value of the annuity. Then the second step, once you find the present value of that annuity at the future date, you find the present value you computed in step one as a single amount. Well, the best way to show you this is to actually show you an example, this two-step process. Okay, how much you will pay for an investment that will pay you six annual payments of $5,000 starting five years from now earning 8%. So here's what you are being promised here. How much will you pay for this investment? But we're not going to pay you anything now. You're going to pay us the money, but you have to find out how much it's, how much you should pay. And we're going to start paying you the money. We're going to start making the payment year five, five years from now. So year five, six, seven, eight, nine, and 10. And we're going to be giving you $5,000. Each axis, $5,000, we're going to be giving you those six annual payments. Okay. And how much you're going to be earning and the period equal to six, six periods and I equal to 8%. Well, the first thing we do using this two-step process is first find the present value of this annuity. Just simply treat it as an annuity. You are standing at year four. Well, n equal to six, i equal to six, i equal to eight, I'm going to go to the present value factor of my table, n equal to six. So this is six, i equal to eight. This is eight. And the present value factor is 4.6229. So simply put, I'm going to take my $5,000, find the present value of those times 4.6229. And let me find the answer for this. So we get 5,000 times 4.6229. And that's equal to 23,114 dollars, 23,114. So at year four, you are standing at year four with 23,114 dollars. We don't care about year four, because this is into the future. We want to know how much is the present value of this payment today. Well, I have to go back and discount this three, two, one, zero. So I have to discount this one, I have to discount it as a single payment, because once I find the present value of the annuity, so the red part is the annuity, now it's a single payment problem. So I have to find the single payment value 23,114. So here n equal to 4, i equal to 8%. And let me find going to the present value of a single amount table, I'm going to have to find the factor n equal to 4, i equal to 8%. And that's 0.735. So if I take this amount times 0.735, that's going to give me 16,989.15. So this is how much I will pay today, or how much this deferred annuity is worth today. If I want to earn 8% and starting to receive the payment five years from now, obviously you can prove it to yourself if you're interested in that. So that's one way in computing the deferred annuity. There's another way that you can compute this deferred annuity by computing the deferred annuity for 10 years, then subtracting four. So one, two, three, four, five, six, seven, eight, nine, 10. Remember the payments don't start until year five. One, two, three, four, five, six. So what you do, another way to do this, this is another method, is to look at this annuity as a 10-year annuity, find the present value of a 10-year annuity, then subtract, then deduct four years from it. Well, what do I mean by this? Well, it means take the $5,000, first assume it's a 10-year annuity. And yeah, you have to, I prefer the two-step because the two-step, you can see what's going on, but here it's the same concept, just you have to be comfortable with what you are doing here. So basically n, so we're assuming here is n equal to 10, i equal to five, and the factor is 6.716.7101, 6.7101. And this is n equal to 10, i equal to eight. And let's see what's the answer for this. Like 5,000 times 6.7101. Well, what we're going to do, we're going to subtract before we do the computation, because there's only to do the computation before we do the subtraction. We can do the computation, they do the subtraction, but let's factor it out. Then we're going to take, we're going to subtract from the total factors, we're going to subtract this part here. We're going to subtract n equal to four, i equal to eight percent. So n equal to four, i equal to eight, and that is 3.3121 minus 3.3121. So let's see. So we have a factor of 6.7101 minus 3.3121, and that's equal to 3.398. Now we'll take the 5,000 times 3.398, and that's going to give us 16,990. Let's see if we are close to the answer. Well, that's at 16,990. At the end of this recording, I'm going to remind you whether you are an accounting student, a finance student, or a CPA candidate. To take a look at my website farhatlectures.com, I don't replace your CPA review course. I'm a useful addition. Your CPA exam is worth it. 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