# Financial Calculator Part 3 - Annuities

Hello everyone. This is Walter Adams and welcome to part three of your calculator lessons here we're going to discuss annuities up until this point we have been ignoring this payment key but we're not going to do that anymore we're going to take a look at what happens when we have an even stream of payments and how we find the present value of these annuities let's say that we have an opportunity to receive \$100 each year over the next three years at 5% interest what would we pay for that today what would be the present value of that stream.

In this case we do not have one single future value number as we did in the last part.

We're going to go down and we're going to take zero and we're going to enter 0 for our future value because we do not have one single value for the future what we do have our future payments that we're going to receive.

We're going to receive 100 and since we're going to receive them in positive terms we're going to put in a positive 100 for our payment.

100 goes into our PMT. This is at 5% interest.

We're going to take 5 we're going to come up and enter it into our interest these payments are going to be received each year for 3 years.

We're going to take 3 we're going to put that into our end just like we've been doing we've got the the information now in our in our top keys and again all we have to do now is hit the present value button and we see that we would pay two hundred and seventy two dollars and thirty two cents now notice that. This is a negative number as we mentioned in the last series meaning that the calculator always assumes that there are positive money and that there are negative monies and in this case we would find it worth it worth our while it would be a value to us of two hundred and seventy two dollars and thirty two cents to pay for that stream of money. Okay, well that's a present value of an ordinary annuity as we mentioned in the earlier calculator series where we receive interest at the as we normally do at the end of the pay period let's clear that data out let's hit our goal button there all and let's do it again as an annuity do where we receive interest at the beginning of the period very simply all we have to do is hit our goal button come up to that beginning and an end that I mentioned to you in a previous episode I hit the beginning end and you now see that I have the word begin in my screen meaning I'm in begin mode.

I do the exact same calculation I have zero for my future value I have 100 for my payment I still have 5% for my interest and we're still doing this for three years.

I have three for my n then I hit the present value button then I see that it's worth two hundred and eighty five dollars and 94 cents which is higher than the present value we calculated before because in an annuity due we're receiving interest at the beginning of the period instead of having to wait until the end of the period.

It's worth more to us that's a basic annuity ordinary annuity and annuity do let's clear that data out by hitting our goal button clear off let's work a couple of other problems let's find out how we find a payment let's say for example that I want to accumulate \$10,000 \$10,000 in the future.

I want to accumulate in this case there's a number of looking for in the future.

I have \$10,000 and I hit my FV and I know that I can receive 6% a year as a rate of return.

I have six I have my interest per year and I'm going to do this for five years I need this \$10,000 in five years.

Five is my n right here.

I've got my data loaded up now the question is what would the payment need to be in order to in order to achieve the accumulation of \$10,000 five years from now I hit the payment key and I see that it's one thousand seven hundred and seventy three dollars and 96 cents that's all there is to it that's the payment I would need to make each year for five years at at five percent err I'm sorry six percent interest to accumulate ten thousand dollars let's clear our data with our gold button clear all let's try one other thing let's say that we still are looking to accumulate the ten thousand dollars in the future.

I hit ten thousand with my future value again and let's say that this time my payment is fixed I can't afford \$1,700 a year but I can afford twelve hundred dollars a year I know that that's what I can afford that's what I'm going to pay each year.

I take twelve hundred and I come up here and I change my sign since. This is what I'm paying out to a negative.

Now I have a negative twelve hundred that I put over here into my payment and let's say then that we're starting with no money.

Much zero is my present value since we're starting with nothing but we're going to make \$1,200 a year payments and I know that I'm going to do this for five years five into my n now the question is what rate of return would I need to earn to take twelve hundred dollars a year for five years and turn that into ten thousand dollars at the end of five years.

I've got my data in I click my interest button that I see that I would have to earn twenty five point seven eight percent in order to accomplish that.

There you have it there you have some of the basics of an ordinary annuity how to doing an annuity do and how to find what payment you would need to accumulate a certain amount of money or what what interest rate you would need to earn if you only had a certain amount of money to put in each year as a payment but that's how we deal with annuities it's quite simple like the rest of the problems we've been doing we put the data into our keys up here and we essentially press the button number of the variable that we're looking for.

I hope that was helpful for you and I look forward then to working with you in the next the next episode we're going to work with uneven cash flows it's going to get real interesting then we're going to use different keys on our calculator hope this was helpful thank you very much we'll see you next time.

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