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In this lecture segment, we're going to be covering the topic of time value of money.

Â Time value tends to be one of the fundamental concepts and

Â in this material, in this lecture will help to support a number of

Â the modules throughout this MOOC course.

Â So some of the learning objectives that we'll cover,

Â we'll split this up in three parts.

Â In part one, I'm going to talk about just the very basics of time value and

Â some of the factors that impact the time value of money.

Â In part two, we'll move on and start looking at some of the specific formulas,

Â some of the specific time value formulas.

Â And in part two, we will focus on the formulas that involve single

Â dollar amounts or single payments in those formulas.

Â And then in part three, we'll finish up with some of the time

Â value formulas that involve multiple payments or

Â a series of payments in determining in the formulas that we use.

Â So first, we're going to start with just some very basics about the time value

Â of money and time value can be captured or summarized by the old phrase.

Â A dollar today is worth more than a dollar tomorrow.

Â So, why is that the case?

Â Well, there's a number of factors that determine why a dollar

Â today is worth more than a dollar tomorrow.

Â The first one and one of the most basic concepts that I think we can all

Â understand is referred to as inflation.

Â Inflation just refers to the fact that the nominal cost or

Â the cost associated with things tends to increase overtime.

Â Inflation is the reason why your grandpa will tell you about why back in his

Â day when candy bars were nickel and gas was $0.30 a gallon.

Â 2:01

Again, it just refers to the fact that the cost of various goods and

Â services tends to increase overtime.

Â The second reason why a dollar today is worth more than a dollar tomorrow is

Â the opportunity cost associated with money or

Â the fact that all of us, if we're given a dollar today.

Â We're going to have some opportunity to invest that money.

Â And hopefully, earn some positive earnings or

Â some positive rate of interest on that investment.

Â So if you give me the choice between giving me a dollar today or waiting and

Â giving me that dollar a year from now, I'm always going to choose the dollar today.

Â Because I can put that dollar into some sort of savings account and

Â have more than a dollar one year from now, so that would make me better off than

Â the alternative of wait until the end of that year to get that dollar.

Â The third factor is risk and uncertainty.

Â So, none of us know what's going to happen tomorrow.

Â Anything we decide to invest our money in today or basically,

Â anything that happens between today and tomorrow or today or

Â any future date, there's some level of risk associated with that.

Â So, all of us would rather have that dollar today rather than taking on

Â the risk of that dollar simply not being there at some point in the future.

Â And in the final factor, it's just related to general human behavior and

Â what we think we know about human behavior and I'm going to refer that as impatience.

Â Every single one of us is impatient in terms of we would rather have things now

Â rather than waiting to get the same thing at some point in the future.

Â So again, all four of these factors are really what serve as the basis for

Â the time value of money and

Â why we say, a dollar today is worth more than a dollar tomorrow.

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Some of the factors that impact time value as we get into the next sections

Â discussing some of the formulas that can be useful to us,

Â as we encounter various time value problems in some of the things we'll be

Â talking about throughout the course.

Â We're going to relate this to what those things actually show up as in some of

Â those time value formulas.

Â So, the first thing I'll talk about is interest rates.

Â So here, we're going to be referring to actual size of the interest rate

Â itself as well as how often interest is calculated or compounded.

Â Both of those factors are going to affect how much more a dollar is worth

Â today than a dollar is worth tomorrow or how big our payment has to be on

Â that loan to pay it off over a specific period of time?

Â Or how much money we need to save to be able to get to a specific target

Â amount at some point in the future?

Â So, interest definitely plays a big role In our time value problems

Â that we encounter in everyday life.

Â The second factor is obviously, time.

Â Time enters is one of the words used in the time value of money phrase.

Â So, how long will you save or invest?

Â That's going to impact how much you need to save in or invest, or

Â how much money you're going to have in the future.

Â Over what time period are you going to pay back a loan?

Â That's going to impact the size of our loan payments.

Â And then finally, value enters into the time value of money.

Â So, how many dollars are we actually talking about?

Â Are those dollars relevant today?

Â So are we referring to or are we concerned with what we would refer to

Â as a present value, or are we talking about

Â dollar amounts that we're concerned with at some point in the future?

Â Some type of future value in terms of the dollars associated with

Â the time value problem or situation that we're considering.

Â And then finally, are we dealing a single amount of money?

Â So are we going to save a single amount today or

Â are we saving to reach a specific amount of future, or we're dealing with

Â a situation where there's going to be a series of payments made,

Â or series of different deposit, or savings amounts that are made overtime.

Â We're going to have formulas that help us deal with each one of those situations

Â Independently.

Â So as we move on to parts two and three of this lecture segment on the time value,

Â we're going to get in to some of those formulas,

Â specifically and look it exactly how those work.

Â First, we're going to focus on the time value formulas that involve

Â a single payment and the two formulas that we're going to cover

Â in this section are basically going to be converting from a single dollar amount

Â today into an equivalent dollar amount in the future.

Â So a problem where we're compounding or

Â converting dollar amounts today to some dollar amount in the future, or

Â we're also going to look at a formula where we are discounting.

Â So based on a future dollar amount, what is the equivalent present value?

Â So the first formula that we'll take a look at is the Single Payment Compound

Â Amount or as an acronym, we can refer to this one as SPCA.

Â What this formula does is it solves for or finds a future value based

Â on a present value, an interest rate and a length of time.

Â So this is going to give us a future value,

Â as long as we know a present value and interest rate in a length of time.

Â Some example where we might find this formula useful.

Â So supposed that you want to fine out if you save or invest $100 today and

Â earn 6% interest, how much money will you have in 10 years?

Â SPCA is a formula that will give you the answer to those types of questions against

Â solving for a few future value based on the present value given an interest rate

Â and a length of time.

Â Again, here we're referring to single dollar amounts.

Â It's a single present value.

Â What is the future value of that,

Â the single future value of that based on an interest rate and a length of time?

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In contrast,

Â we can also do the same type of thing in terms of moving backwards in time.

Â So what is the present value of a future dollar amount given a time

Â period that separates those two, as well as an interest rate?

Â The formula that we would use in that case is referred to as

Â the Single Payment Present Value or the SPPV formula.

Â Again, this formula is used to find the present value of a single

Â future dollar amount given an interest rate in a length of time.

Â So, situations are questions where this SPPV formula might be useful.

Â Let's say, you'd like to have $1,000 in five years.

Â So, that's the future value that you know or the targeted future value.

Â How much would I need to save today?

Â How much would I need to put away today,

Â if I can earn 5% interest over that five year period?

Â The SPPV formula would help us to solve for that required present value, so

Â that we would have that $1,000 five years from now.

Â In this section, we're going to be covering some more time value formulas.

Â Specifically, ones that involve series of payments over a period of time.

Â So the first one we'll take a look at is called the Uniform Series Compound Amount

Â formula or USCA, as our acronym.

Â What this formula does is it solves for a future value based on a series of payments

Â that are made over a certain period of time earning a specific interest rate.

Â So, examples where we might use this formula or

Â cases where this formula might be useful in terms of handling time value problems.

Â If I save $100 each month,

Â how much will I have in ten years if I can earn 6% interest?

Â That question includes a regular payment,

Â that's the $100 that will be saving or making each month.

Â We're going to do that over a ten year period and

Â we're going to earn 6% interest on each one of those monthly savings amounts.

Â How much will we have in 10 years?

Â The USCA formula can be use in this case to tell us how much we'll have at that

Â future time period.

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We can also rearrange the USCA formula to solve for

Â the payment based on a specific or target future value and

Â that formula is referred to as the Sinking Fund Deposit, or SFD formula.

Â Again, here, we're going to use this formula to find the required

Â payment size based on a known or targeted future value.

Â So, real common example here would be where you know that that there is

Â a certain amount of money that you want to have in the future.

Â You have a savings goal or a savings target.

Â You want to know how much do I need to regularly save, so

Â that I do have that amount of money in the future?

Â So the example I have here is if you would like to have $50,000 in 18 years to help,

Â maybe pay for a portion of your child's college cost,

Â how much are you going to need to start saving each month today?

Â So beginning today,

Â how much do you need to start saving each month if you can earn 5% interest?

Â So that in 18 years, you have that $50,000.

Â Another really common example where the Sinking Fund Deposit formula is used

Â is for retirement planning.

Â So, let's say that you know how much money you would like to have at retirement.

Â Maybe that's 30 or 40 or 45 or even 50 years out in the future, but

Â you can have an idea of how much money you would like to have saved up at retirement.

Â If you have an interest rate that you think you can earn on the money you're

Â putting away for retirement, then again, the length of time between now and

Â when you will retire and that target future value that you'd like to have.

Â You can enter those things in the Sinking Fund Deposit formula to get an idea of

Â how much you need to be saving regularly between now and the time you retire, so

Â you actually achieve or accumulate that targeted retirement savings.

Â Moving on to discounting formulas or

Â formulas that are going to find present values based on series of payments.

Â We're going to start with the Uniform Series Present Value formula or USPV.

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So, an example here where we might us the USPV formula is let's say that you're

Â an individual who has reached retirement age.

Â You have a certain amount of money saved they in your retirement account and

Â you would like to know how long that money will last if you take out a certain amount

Â to cover living expenses, and other things each month?

Â So to put down specific examples,

Â how much of money saved in my retirement account if I can earn 5% interest and

Â I would like to withdraw $2,000 each month during retirement?

Â Again, what this will do is based on that $2,000 regular payment or

Â withdrawal that you'll be making during retirement.

Â The length of time that you may think you may be in retirement and

Â the 5% interest rate that you're assuming that you can earn.

Â You can use the USPV formula to determine

Â how much money is actually needed at retirement age.

Â Finally, again, we can do some rearranging with that USPV formula.

Â And instead of trying to find the present value, we can work and

Â try to find the payment associated with a specific present value.

Â So this formula is referred to as the Capital Recovery or CR formula or

Â sometimes more commonly, it's referred to as the Loan Amortization formula and

Â there's a good reason for that.

Â So that what this is going to do is again,

Â find the payment that is associated with a specific present value and

Â one of the most common examples or situations where this formula

Â becomes useful or is used is to calculate the payment associated with a loan.

Â So again,

Â that's why this is often referred to as the Loan Amortization formula.

Â So for example, let's say that you're planning on borrowing $100,000 on a home

Â mortgage, you're going to pay that off over a 30 year term and

Â the interest rate on that loan is 6%.

Â You could use that information along with the Loan Amortization formula to find

Â what the monthly payment is for that loan contract.

Â So how much would you need to pay each month on that $100,000 loan if you're

Â being charged 6%, so that you'd have that loan paid off over that 30-year term?

Â So, this is the formula that's used by your lender to determine

Â the Loan Amortization schedule on any loan contracts you use.

Â How much you're borrowing, the interest rate and

Â the term length will be used with this formula to determine what your minimum

Â regular payment will be on that loan contract.

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