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