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馃敶 Annuity Calculation in 9 Minutes - Annuities Explained for Present Value of an Annuity Formula - YouTube
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Annuity Calculation in 9 Minutes - Annuities
Explained for Present Value of an Annuity
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Formula
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Okay.
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Welcome once again to MBAbullshit.com.
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So our topic for this video is the present
value of annuity.
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Okay?
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So, remember you can always go back to MBAbullsit.com.
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Now, before this video, you should already
understand present value and net present value.
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If you don鈥檛 understand it yet, you can
watch the other free videos on these topics
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above.
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Alright, so let鈥檚 get down to it.
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Okay.
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Let鈥檚 start with the question: What if the
bank deposit rates outside also known as the
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discount rate, maybe, are now at five percent
per year or per annum?
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Okay?
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Per annum means per year.
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And what if someone offered you a sure investment
which would give you one hundred dollars in
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the first year, one hundred dollars in the
second year and one hundred dollars in the
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third year?
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Okay?
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So each payment is equal to each other and
it is for a set number of years.
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Exactly three years.
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Now, how much is this investment worth?
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Okay?
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Well we already know from the present value
and net present value formulas that the investment
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is worth one hundred multiplied by one point
zero five meaning five percent raised to the
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negative one for year one and raised to the
negative 2 for year two, raised to the negative
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three for year three, and we will find that
this investment using the net present value
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formula is two hundred seventy-two dollars
and thirty-three cents.
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Okay?
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So this investment is called the annuity,
alright?
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It is equal payments every period, every period.
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It is usually every year and it is set for
a certain number of years or a certain number
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of periods.
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Okay?
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It is not forever.
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Okay.
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Now this two hundred seventy-two dollars and
thirty-three cents over year is called the
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present value of an annuity.
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Okay.
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So it鈥檚 simple.
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Okay?
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But it was simple because it was only three
payments.
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What if it happened to be a lot more than
three years?
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Like maybe thirty-two years?
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Okay?
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It will be two long, alright?
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It will be too long to use the present value
formula for each payment.
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Okay?
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Imagine if we had to type, we had to write
down this plus this plus this for thirty-two
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years all the way there and continuing, and
continuing.
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Okay?
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That would take way too long.
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So luckily, we have a short cut formula and
looks like this.
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Oh, it鈥檚 scary formula, right?
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Look at it.
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It looks really freaky.
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Alright?
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Now, there鈥檚 actually an even scarier version
than this, okay?
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Your professor might use a different formula
than this but it鈥檚 still the same as this
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as long as he says it鈥檚 the present value
of an annuity formula, it鈥檚 actually the
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same as this but it might be even longer.
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Okay?
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Or crazier but mathematically, it will be
the same.
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Now, okay.
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Here鈥檚 an even easier one which I use.
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I don鈥檛 know.
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I don鈥檛 think I invented that.
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I鈥檓 sure somebody else also made it but
here鈥檚 an easier one which I use.
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Alright?
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Now don鈥檛 panic.
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It still looks scary but it鈥檚 actually much
easier to do when you use a calculator or
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a scientific calculator, and it looks like
this.
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Oh, what鈥檚 this?
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Alright.
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Now the first thing I want you to remember
is that this X over here and this X over here
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means multiplication, okay?
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It is not a variable, okay?
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It is not the variable X.
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It just means one times R. Or one multiplied
by R. Same thing here.
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It means one multiplied by R.
Okay.
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So if we do that, okay, if we use this formula
it becomes easy as pie and let me show you.
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Okay?
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So based on the earlier example, the present
value over annuity is one hundred dollars,
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okay, which is the cash payment or cash flow
over here multiplied by one which is given
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in the formula multiplied by the rates of
the bank or the discount rate which is five
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percent or zero point zero five raise to the
negative one which is given minus, okay, again
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one which is given multiplied by zero point
zero five which is the rate over here raised
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to the negative one which is also given multiplied
by one plus R which is the same as one point
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zero five, okay?
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One point zero five is the interest rate of
five percent raised to the negative N or the
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negative number of years, and we already said
it was thirty-two years.
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So raised to the negative thirty-two.
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And if we do this altogether, we multiply
this whole and put a subtraction over here,
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okay?
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On your calculator, you will get the amount
of one thousand five hundred eighty dollars.
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So now you know the present value of an annuity.
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Okay?
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Now a note is that if your calculator sucks
okay?
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If your calculator sucks then you cannot do
a negative exponent like this and so you will
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have to do it the long way using this.
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Now I highly recommend you get a good scientific
calculator.
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It is not an expense.
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It is a good investment.
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Alright?
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So get a good scientific calculator which
can do negative exponent signs like this,
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and then you鈥檒l be able to compute this
thing over here in a jiffy.
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Alright?
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So there you have it.
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The present value of an annuity.
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Now that you understand the basic concept
of present value of an annuity, you are ready
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for our next video on present value of a growing
annuity and also other annuity problems such
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as delayed annuity, an annuity due, infrequent
annuity, comparison of the annuities, etcetera,
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and you can find those on our MBAbullshit.com.
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Alright.
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So for this video, I hope you liked it.
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Please share it and on Twitter, you could
follow us.
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Our nickname is MBAbullshit.
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Have a great day and good bye.
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