How to Calculate the Future Value of an Annuity

all else held constant, the future value of an annuity will increase if you: This is a topic that many people are looking for. star-trek-voyager.net is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, star-trek-voyager.net would like to introduce to you How to Calculate the Future Value of an Annuity. Following along are instructions in the video below:

“This video. I m going to show you how to calculate the future value of of an annuity. An annuity simply is a series of equal ongoing payments that we contribute to a particular investment. It s very very common particularly with 401ks and for 3 b.

s. Where not only do we invest an initial lump sum into an investment. But we also contribute a series of ongoing payments and a lot of times those can be in equal amounts. Because typically it s a percentage of our annual income and so what i m going to do is show you how to calculate that using a long hand method that we would use to calculate for such a future value of an annuity.

It s a very very simple process it can be quite tedious. One thing. I will say is if you have not seen the prior video that i posted with regards to calculating the future value an ab investment. I would encourage you to review that because we do build upon some of that material.

It s very brief only approximately 5 to 6 minutes. And it ll definitely catch you up to speed. So that you re ready to go for this particular problem here so the first thing that we need to do is we need to figure out ultimately what we re going to invest if you remember from last time. We ve talked about the different types of variables that we need to consider with regards to calculating future values of investments.

The first thing that we need to know ultimately is what is going to be our present value you know what is the amount that we re going to contribute today to our particular investment and so let s just say that the present value of our investment is going to be 10000. That s the money that we re going to contribute today to this particular investment. We also need to know ultimately how long we re going to invest our money s and so let s just say that we re going to invest this for 5 years. And as far as interest rate.

We re going to assume that will earn a 7 percent interest rate compounded annually..


Now so far this is very similar to how you would calculate the future value of a lump sum investment. The difference though is that we have to deal with that series of ongoing payments that we re actually going to be making and so we abbreviate that as pmt. Some some methods are also abbreviated as c. Which stands for generally cash flow pmt is a common abbreviation and act.

It s a symbol usually on most financial calculators. So i use that just for consistency purposes. Since you usually see it across different different forms. So let s assume that our payment or what we re going to pay on an annual basis.

Let s just say that s going to be a thousand dollars. And so we re going to invest. Ten thousand dollars. Initially contribute one thousand dollars every year for five years earning a interest rate of approximately seven percent compounded annually.

So let s go through altom utley. How we would solve this particular problem first thing. I want to do and what we need to do here. First is kind of draw out just a basic line here because we re going to chart our payments and so i m going to start with a line just going all the way across here and then we re going to do is put some hash marks.

Here to symbolize the first pair that today. The first period second third fourth and in that last period. And if we want to we can go ahead and even abbreviate each one and list. What they are just so there s no confusion now we want to do also is want to list when each of the payments are going to be made this helps us v.

Very very organized so that we ultimately can get to the right answer..


Which is what we re after and so in the zero period. Which stands for today. We are going to be putting in our ten thousand dollars. Okay in the first period which is in the first year.

We re going to be investing a thousand dollars and we re going to do that the same thing four years two three four and five okay and i m going to show you ultimately how this plays effect. Now what we have to do is we have to ultimately compound. These to that fifth year because that s where we re ultimately trying to figure out how much money we end up after that period of time. And so.

The first thing that we start with we always start with the the latest or closest to that fifth year. So we re going to start year five we already are going to contribute 1000. And so this was going to be quite easy because we re going to calculate basically the future value of a lump sum investment that s how we re going to treat this as and so we re going to take our thousand dollars we re going to multiply it by one plus our interest rate of 007 to the nth power. Which in this case is going to be zero.

Because we re investing it in the fifth year. So it s not going to have the time to actually grow and so here we re actually just going to go ahead and get our our 1000. Dollars back so we re not really getting anything with this particular investment which is fine. We just put the money in so we re not allowing it time to grow.

It will grow in subsequent years. Assuming we leave this this money in the investment. But let s do the same thing for each of these periods here and so first we re going to take our 1000. Dollars in year four we re going to move this over and we re going to do the same type of equation.

The future value of a lump sum and the only difference here is that we re going to change the period..


Which is n. And so instead of being zero. This is actually going to be one. And so we re doing 1 plus 0.

7 to the first power times 1000. And if you do that quick calculation you re going to find that we end up with an end result of one thousand seventy dollars. Okay little higher than before we do the same thing in year three so we re going to take this over or basically going to compound this for two years since we re already in year three now we have to compound this for two years because we re going once to year four and the next. We re going to year five.

So that s two years right there so let s go ahead and work out that problem so let s take. 1000 just like before times one plus our interest rate of 007 and this is going to be to the second power and that s going to get us. 1000 14490 okay and then next we re going to that with your two and you can see kind of wyatt while i m calculating this just how tedious this becomes and how why you would utilize the equation. If you had more than just a handful of years because this can get to be a rather long process as i m kind of going through this here.

But it s important to understand simply how the process works and then you can use the formula and at least you can understand ultimately how you got there because you know how to work out the problem by hand. Which i think is very important and so the last one here we have is year four. We do that same process here bring that thousand dollars over we re going to go by to the fourth power. And that s going to give us one thousand three hundred ten dollars as well as eighty cents.

And so we re almost done here actually you can see that we have quite a bit of information already and the only thing that we need to do left. And we re going to move this up a little bit just so we have some more room. The only thing else we need to do is we need to actually take our ten thousand dollars. And we also need to compound that to the fifth year and so we re going to move this over and do the same exact thing that we did with the other numbers before and so instead of being a thousand.

It s going to be ten thousand we re going to add that to one plus our interest rate of seven percent to the fifth power..


And that s actually going to get us 14. Thousand twenty five dollars and 52 cents. And so the last thing that we need to do actually is just go ahead and add all these together so we draw one line right here and then ultimately add all of our future value cash flows that we have and so if you add all these together. What you do get is a final value of 19 thousand seven hundred and seventy six dollars and 26 cents.

Okay let s make sure that s a nine and so what this would mean is that if we invested a 10000. Lump sum. Initially one thousand dollars on an annual basis for five years assuming that we grew our interest or grew our investment at seven percent compounded annually. We would actually end up with nineteen thousand seven hundred and seventy six dollars and twenty six cents.

Now the beauty of this particular format or form of solving this problem. Too is that you can also assume that your cash flows are different. We assumed that they were ongoing but also the same amount and you can have inconsistent cash flows. Where maybe in year one we invest a thousand maybe in year two we invest 1500 maybe in your three.

It s a little different. And so using this type of form to actually solve that problem you can change those figures and ultimately compound those by the number of years that you need to to ultimately get to the right answer. There are also a number of ways to solve them using financial calculators. Which of course if you re going to use a financial calculator use.

But this is ultimately how you would calculate the future value of an annuity utilizing. The ” ..

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