 Hello, and welcome to this session. This is Professor Farhad. In this session, we would look at applications of the time value of money, part two. This topic is covered in introductory financial accounting courses, as well as intermediate accounting, managerial accounting, as well as corporate finance or introduction to finance. Also covered on the CPA exam. As always, I would like to remind you to connect with me on LinkedIn. If you haven't done so, YouTube is where you would need to subscribe. I have 1,600 plus accounting, auditing, finance, and tax lectures. This is a list of all my courses, including many CPA questions. If you like my lectures, please like them, share them, subscribe, put them in playlists, connect with me on Instagram. If these lectures are helping you, it means they might help other people, so share the wealth. On my website, farhadlectures.com, you will find additional resources and supplementary material that's going to help you succeed in your accounting education, as well as your CPA exam. I strongly suggest you visit my website. For this recording, you will need the time value of money concept as a prerequisite. The link for those sessions are in the description, is in the description below. Make sure to check it out in case you are not familiar with the concept of the time value of money. So let's take a look at part two. This is part two. I already worked part one, so if you're not sure, look in the description. You can see part one if you're interested in practicing those exercises. So let's look at part two. And part two, also a series of questions that's going to illustrate the time value of money. Let's take a look at the first question. For each of the following situation, identify whether the case is either a present value or future value, a single amount or an annuity, the table you would use in your computation, but do not solve. I'm going to go ahead and solve anyhow, sorry, in the interest rate time period you would use. So basically, we're going to go over each one of them and solve it anyhow. Let's look at A. You need to accumulate $10,000 for a trip you wish to take in four years. Hopefully the coronavirus will be done by that time. You're able to earn 8% compounded semi-annually on your savings. Excellent. So the first thing I know is the interest rate is 8% since it's compounded semi-annually it's 4%. So I equal to 4%. You plan to make one deposit and let the money accumulate for four years. So this is you're only making a single deposit. So we are looking at a single amount. What amount? How would you determine the amount of one deposit? Well, so you need 10,000. You need 10,000. How much do you need to invest today? And you can invest this money for the I is compounded semi-annually which is 4% and the N they say for four years. Four years is eight periods. So four years is eight periods because you're going to be that money it's going it's going to accumulate every six months. So how much money you will deposit today? And I'll have to make the I'm going to have to show you the computation although they don't they don't show you this. Well how would you do so easy? I'm going to take my amount go to my present value of a dollar amount I equal to 4 and equal to 8 and equal to 8 and the factor is 7,300.7307. So if I take 10,000 times 0.7307 I should get 7,307 dollars. So today I should invest 7,307 dollars. Now I'm going to have to show you the computation for sure because I want to show you how the compounding work. So let's go to the Excel sheet. So my answer was 7,307 dollars. Now what I said is this I'm going to have period one, period two. I'm going to have remember I said I'm going to have eight periods and each period because it's four years but semi-annually eight periods and I equal to 4 percent. So here's what's going to happen. This money the 7,307 after six months later it's going to grow at 1.04 it's going to grow at 4 percent. Then I'm just going to drag the formula it's basically what I'm going to be doing six months later it will grow to 7,903 the previous amount times 1 plus 0.4 and if I drag it all the way notice the amount is 10,000 dollars. So notice because it's compounded semi this is compounded semi-annually. So I will need today 7,307 dollars. So what I did simply put what I did is I used my present value table to figure it out to figure it out. Now what else I can do I can take the 10,000 I can take the 10,000 and go to my future value table I can go to my future value table. I equal to 4 percent and equal to 8 and it's 1.368. So if I take my 10,000 let's do the math and I divide 10,000 by 1.3686 that's going to give me 7,306 dollars that's fine that's good enough for me. Notice it's the same answer so I could use either the present value table or the future value table. I would use the present value because they're giving me the future value I'd like to use the present value but you could use both remember they're the reciprocal of each other this is what I talked about in the discussion. Now let's take a look at part B assume the same fact in part A except that you will make semi-annual deposit to your savings account so simply put in part A we said if you deposit 7,307 dollars you would receive 10,000. Now what happened in part B in part B saying let's assume you're going to be making one two three four five six seven eight one two three four five six seven eight you're going to be making eight payments eight payments to get to 10,000 dollar how would you find out what's your payment here we are dealing with n equal to same thing as the part A n equal to eight it's four years but it's semi-annual i equal to four percent we know that from if we take the payment once we find the payment times the factor that's going to give us the future value we don't know the payment payment is the x can we find the factor sure we can this is a future value problem we go to the future value annuity table future value annuity table and in this problem we have n equal to eight eight periods at four percent and the factor is 9.2142 so the factor is 9.2142 so let's go ahead and 9.2142 that's going to give us 10,000 dollar now if we solve for x 10,000 divided by the factor 9.2142 it's going to give us a payment approximately 85 dollars at 1,085 dollars now the best way to to prove this is also to show you on an excel sheet so let's go ahead and do so so remember in the prior problem we needed seven thousand and three dollars now let's take a look at this so we're going to have eight payments and we're going to be adding payments to the balance payment plus balance and we're going to have the interest rate of four percent the interest rate is four percent and we're going to have the balance column for the balance so let's do this and see if indeed 1,085 dollars will get us where we need to do we'll get us where we need to get which is 10,000 dollar so we have payment one payment two we have eight payments so I'm just doing the math proof just to kind of show you that is what it is first I have 1,085 and 25 set 28 set to be more specific this money is going to grow at four percent oops four percent so I'm going to I'm going to be making the first payment six months later it's going to it's going to grow at six percent and it's going to grow to be this amount times one plus four percent remember I need my original amount it's going to grow to be 1,128 what I'm going to do I'm going to take this this balance and add to 1,085 six months later and I'm going to let it grow also at four percent and this amount it's going to grow to be 2,302 and what I'm going to do I'm going to drag the formula you guys see what what I'm doing here I'm going to drag the formula here I'm going to drag the formula here and four percent it doesn't matter 0.04 or four and I'm going to drag the formula here and if you notice if I keep adding 1,085 let it grow at four percent at 1,085 let it grow at four percent at 1,085 after eight payment I will have approximately $9,997 okay so this is how we found the value of this the payment which is the payment is what they're asking us is for the payment so I need to make a payment of approximately 1,085 eight payments it will get me approximately 10,000 that's the other way if I don't have 7,307 now to invest all at once often people don't have the money they will save and now you find out exactly how much you will need to save for that hopefully this makes sense to you let's take a look at number C C as in Charlie you want to retire after working 40 years with savings and access of a million so your goal is to have a million you expect to save four thousand a year for 40 years and earn an annual rate of eight percent will you able to retire with more than a million in 40 years well basically what are they asking us here they're asking us if you invest four thousand every year for 40 years and your money earning eight percent will you have a million that's your goal so simply put on again I like always I like to always show you this on a graph because hopefully it makes sense so this is one two three four five six seven eight nine ten eleven twelve thirteen fourteen seventeen eighteen nineteen twenty twenty one twenty two twenty three twenty four twenty five twenty six twenty seven twenty eight twenty nine thirty thirty one thirty two thirty three thirty four thirty five thirty six thirty seven thirty eight thirty nine forty so you're going to be making forty each of these is four thousand and if you make those four thousand dollar payment will you have a million dollar if you invest this money at at eight percent well how would I know well I'm going to take four thousand it's an annuity times the few future value annuity n equal to forty i equal to eight percent so four thousand times that so let me go to the future value and find out if I can do it or not let's see let's see n equal to forty i equal to eight percent so I'm going to take four thousand times two fifty nine and point oh five oh five oh five okay so let's see if that's enough for me to retire if I take four thousand times two fifty nine point oh five oh five and that's going to give me one million thirty six thousand yes I should be fine one million approximately one million thirty six thousand yes I should be fine I should have my million dollars so let's take a look at number d a sweepstake agency names you names you a grand price winner you can take 225 immediately now or elect to receive an annual installment of thirty thousand dollar for twenty twenty years you can earn ten percent which of these prices do you choose so here we are making a we are making a an analysis a decision should we take the 225 now or should we take 30 000 for the next 30 years so here's option one option one you don't need to do anything 225 option two I need to find 30 000 times the present value annuity factor n equal to 30 I'm sorry n equal to 20 I equal to 10 percent that's basically so so 225 versus if I wait and get this money later in 30 000 would I would I be better off it pretty straightforward analysis in a sense so let's take a look at it so on the present value annuity factor n equal to 20 I equal to 10 present value annuity I have n equal to 20 I equal to 10 and the factor is 8.5136 so 30 000 times 8.5136 let's see if that is that is see which one is better 30 000 times 8.5136 that's equal to 225 408 practically the same 225 408 guess what it doesn't matter it doesn't really matter so simply put if you take option one today take 225 today or wait to get 20 30 000 assuming you can earn 8 percent on your 10 percent it's it doesn't matter it those are the same amount so which choose the which prize do you choose I don't know which prize do you choose I'll take the 225 today or I don't know I don't know 10 percent is pretty good 10 percent if you know because they're they're basically option two they're guaranteeing 10 percent and I you know the goal is can you get this money today can you get the 225 today and earn more than 10 percent so this is what basically boils down to can you make an investment where you could earn more than 10 percent if you can take option one if you cannot if you cannot find an investment whether it's in stocks bonds real estate start your own business deposit that money in the bank and 10 percent is pretty tempting okay I'm not sure I'm not really sure what I would do okay that's for you to decide congratulations for winning okay um as always um visit my website in the next three quarter I'm thinking about looking at excel sheet showing you how to solve this problem in excel sheet annuity problems present values and if you're studying for your CPA exam as always study hard especially for your courses accounting is worth it and stay safe during those coronavirus days