[MUSIC] In this lecture segment, we're going to be covering the topic of time value of money. Time value tends to be one of the fundamental concepts and in this material, in this lecture will help to support a number of the modules throughout this MOOC course. So some of the learning objectives that we'll cover, we'll split this up in three parts. In part one, I'm going to talk about just the very basics of time value and some of the factors that impact the time value of money. In part two, we'll move on and start looking at some of the specific formulas, some of the specific time value formulas. And in part two, we will focus on the formulas that involve single dollar amounts or single payments in those formulas. And then in part three, we'll finish up with some of the time value formulas that involve multiple payments or a series of payments in determining in the formulas that we use. So first, we're going to start with just some very basics about the time value of money and time value can be captured or summarized by the old phrase. A dollar today is worth more than a dollar tomorrow. So, why is that the case? Well, there's a number of factors that determine why a dollar today is worth more than a dollar tomorrow. The first one and one of the most basic concepts that I think we can all understand is referred to as inflation. Inflation just refers to the fact that the nominal cost or the cost associated with things tends to increase overtime. Inflation is the reason why your grandpa will tell you about why back in his day when candy bars were nickel and gas was $0.30 a gallon. Again, it just refers to the fact that the cost of various goods and services tends to increase overtime. The second reason why a dollar today is worth more than a dollar tomorrow is the opportunity cost associated with money or the fact that all of us, if we're given a dollar today. We're going to have some opportunity to invest that money. And hopefully, earn some positive earnings or some positive rate of interest on that investment. So if you give me the choice between giving me a dollar today or waiting and giving me that dollar a year from now, I'm always going to choose the dollar today. Because I can put that dollar into some sort of savings account and have more than a dollar one year from now, so that would make me better off than the alternative of wait until the end of that year to get that dollar. The third factor is risk and uncertainty. So, none of us know what's going to happen tomorrow. Anything we decide to invest our money in today or basically, anything that happens between today and tomorrow or today or any future date, there's some level of risk associated with that. So, all of us would rather have that dollar today rather than taking on the risk of that dollar simply not being there at some point in the future. And in the final factor, it's just related to general human behavior and what we think we know about human behavior and I'm going to refer that as impatience. Every single one of us is impatient in terms of we would rather have things now rather than waiting to get the same thing at some point in the future. So again, all four of these factors are really what serve as the basis for the time value of money and why we say, a dollar today is worth more than a dollar tomorrow. Some of the factors that impact time value as we get into the next sections discussing some of the formulas that can be useful to us, as we encounter various time value problems in some of the things we'll be talking about throughout the course. We're going to relate this to what those things actually show up as in some of those time value formulas. So, the first thing I'll talk about is interest rates. So here, we're going to be referring to actual size of the interest rate itself as well as how often interest is calculated or compounded. Both of those factors are going to affect how much more a dollar is worth today than a dollar is worth tomorrow or how big our payment has to be on that loan to pay it off over a specific period of time? Or how much money we need to save to be able to get to a specific target amount at some point in the future? So, interest definitely plays a big role In our time value problems that we encounter in everyday life. The second factor is obviously, time. Time enters is one of the words used in the time value of money phrase. So, how long will you save or invest? That's going to impact how much you need to save in or invest, or how much money you're going to have in the future. Over what time period are you going to pay back a loan? That's going to impact the size of our loan payments. And then finally, value enters into the time value of money. So, how many dollars are we actually talking about? Are those dollars relevant today? So are we referring to or are we concerned with what we would refer to as a present value, or are we talking about dollar amounts that we're concerned with at some point in the future? Some type of future value in terms of the dollars associated with the time value problem or situation that we're considering. And then finally, are we dealing a single amount of money? So are we going to save a single amount today or are we saving to reach a specific amount of future, or we're dealing with a situation where there's going to be a series of payments made, or series of different deposit, or savings amounts that are made overtime. We're going to have formulas that help us deal with each one of those situations Independently. So as we move on to parts two and three of this lecture segment on the time value, we're going to get in to some of those formulas, specifically and look it exactly how those work. First, we're going to focus on the time value formulas that involve a single payment and the two formulas that we're going to cover in this section are basically going to be converting from a single dollar amount today into an equivalent dollar amount in the future. So a problem where we're compounding or converting dollar amounts today to some dollar amount in the future, or we're also going to look at a formula where we are discounting. So based on a future dollar amount, what is the equivalent present value? So the first formula that we'll take a look at is the Single Payment Compound Amount or as an acronym, we can refer to this one as SPCA. What this formula does is it solves for or finds a future value based on a present value, an interest rate and a length of time. So this is going to give us a future value, as long as we know a present value and interest rate in a length of time. Some example where we might find this formula useful. So supposed that you want to fine out if you save or invest $100 today and earn 6% interest, how much money will you have in 10 years? SPCA is a formula that will give you the answer to those types of questions against solving for a few future value based on the present value given an interest rate and a length of time. Again, here we're referring to single dollar amounts. It's a single present value. What is the future value of that, the single future value of that based on an interest rate and a length of time? In contrast, we can also do the same type of thing in terms of moving backwards in time. So what is the present value of a future dollar amount given a time period that separates those two, as well as an interest rate? The formula that we would use in that case is referred to as the Single Payment Present Value or the SPPV formula. Again, this formula is used to find the present value of a single future dollar amount given an interest rate in a length of time. So, situations are questions where this SPPV formula might be useful. Let's say, you'd like to have $1,000 in five years. So, that's the future value that you know or the targeted future value. How much would I need to save today? How much would I need to put away today, if I can earn 5% interest over that five year period? The SPPV formula would help us to solve for that required present value, so that we would have that $1,000 five years from now. In this section, we're going to be covering some more time value formulas. Specifically, ones that involve series of payments over a period of time. So the first one we'll take a look at is called the Uniform Series Compound Amount formula or USCA, as our acronym. What this formula does is it solves for a future value based on a series of payments that are made over a certain period of time earning a specific interest rate. So, examples where we might use this formula or cases where this formula might be useful in terms of handling time value problems. If I save $100 each month, how much will I have in ten years if I can earn 6% interest? That question includes a regular payment, that's the $100 that will be saving or making each month. We're going to do that over a ten year period and we're going to earn 6% interest on each one of those monthly savings amounts. How much will we have in 10 years? The USCA formula can be use in this case to tell us how much we'll have at that future time period. We can also rearrange the USCA formula to solve for the payment based on a specific or target future value and that formula is referred to as the Sinking Fund Deposit, or SFD formula. Again, here, we're going to use this formula to find the required payment size based on a known or targeted future value. So, real common example here would be where you know that that there is a certain amount of money that you want to have in the future. You have a savings goal or a savings target. You want to know how much do I need to regularly save, so that I do have that amount of money in the future? So the example I have here is if you would like to have $50,000 in 18 years to help, maybe pay for a portion of your child's college cost, how much are you going to need to start saving each month today? So beginning today, how much do you need to start saving each month if you can earn 5% interest? So that in 18 years, you have that $50,000. Another really common example where the Sinking Fund Deposit formula is used is for retirement planning. So, let's say that you know how much money you would like to have at retirement. Maybe that's 30 or 40 or 45 or even 50 years out in the future, but you can have an idea of how much money you would like to have saved up at retirement. If you have an interest rate that you think you can earn on the money you're putting away for retirement, then again, the length of time between now and when you will retire and that target future value that you'd like to have. You can enter those things in the Sinking Fund Deposit formula to get an idea of how much you need to be saving regularly between now and the time you retire, so you actually achieve or accumulate that targeted retirement savings. Moving on to discounting formulas or formulas that are going to find present values based on series of payments. We're going to start with the Uniform Series Present Value formula or USPV. This formula is going to help us find the present or the current value of a series of payments that are going to be made over a certain length of time at a given interest rate. So, an example here where we might us the USPV formula is let's say that you're an individual who has reached retirement age. You have a certain amount of money saved they in your retirement account and you would like to know how long that money will last if you take out a certain amount to cover living expenses, and other things each month? So to put down specific examples, how much of money saved in my retirement account if I can earn 5% interest and I would like to withdraw $2,000 each month during retirement? Again, what this will do is based on that $2,000 regular payment or withdrawal that you'll be making during retirement. The length of time that you may think you may be in retirement and the 5% interest rate that you're assuming that you can earn. You can use the USPV formula to determine how much money is actually needed at retirement age. Finally, again, we can do some rearranging with that USPV formula. And instead of trying to find the present value, we can work and try to find the payment associated with a specific present value. So this formula is referred to as the Capital Recovery or CR formula or sometimes more commonly, it's referred to as the Loan Amortization formula and there's a good reason for that. So that what this is going to do is again, find the payment that is associated with a specific present value and one of the most common examples or situations where this formula becomes useful or is used is to calculate the payment associated with a loan. So again, that's why this is often referred to as the Loan Amortization formula. So for example, let's say that you're planning on borrowing $100,000 on a home mortgage, you're going to pay that off over a 30 year term and the interest rate on that loan is 6%. You could use that information along with the Loan Amortization formula to find what the monthly payment is for that loan contract. So how much would you need to pay each month on that $100,000 loan if you're being charged 6%, so that you'd have that loan paid off over that 30-year term? So, this is the formula that's used by your lender to determine the Loan Amortization schedule on any loan contracts you use. How much you're borrowing, the interest rate and the term length will be used with this formula to determine what your minimum regular payment will be on that loan contract. [MUSIC]