# Future Value Of Money

In this post, we are going to talk about the future value of the annuity. This post is a part of a post series where we are discussing the time value of money In this first post, I’ve talked about the basics of the time value of money. Then we’ve talked about future value. Normal future value, suppose if you do a one-time payment somewhere so how much will be its future value after a certain time period at a certain interest rate? Now the future value of annuity means you keep investing a fixed amount every month somewhere then how much will its future value be? For example, let’s say you deposit Rs.10,000 every month suppose you are 24-25 years old so what will be the total amount when your retire after 24-25 years? We will understand its calculation in this post. So stay reading this post from the beginning to the end.

Let’s go straight to the Post. Let’s understand the future value of an annuity with the help of an example Let’s assume, in one year, let’s say its May 2018, And let’s take a period of 3 years i.e May 2019 and May 2020 Now, let’s assume you invest Rs.10,000 every year. So you invested 10,000 in the first year. and the second and third years also you invested Rs.10,000. Now we will see, how much will our money be in May 2020. this is 2020 this is 2020. So see, this is your investment, right So you invested this amount of money now how much will your value be? Now how will we find its value? I’ve told you the formula of the future value in the last post. So future value is the present value multiplied by raised to the power.

So this is the present value here. Let’s take the rate of interest as 7% on FD We have invested this money in the FD which is giving us the returns of 7% annually. So how will we calculate this? Our future value will be… Let’s understand according to the timeline here This money will be invested for 2 years, right? This money is invested for 2 years from May 2018 to May 2020. You invested the money for 2 years in May 2018. And the money you deposited in 2020 got invested for zero time, right? So we will calculate our present value according to that only. 10,000 multiplied by since the rate of interest is 7% here so we’ll write 0.07 here raised to the power 2 since we’ve talked about 2 years here. Similarly, we’ll write 10,000* raised to power 1 because this money has been invested for 1 year here. here it will be 10,000 only because the power will be 0 so it’ll be the same 10,000 only so if you’ll do its calculation, your value will be Rs.11,449. And this value will be 10,700. And this value is 10,000.

So if you do the total, then the total value will be Rs.32,149. So, in the third year, you’ll get Rs.32,149. Not see when you’ll do the investment for the merger time period and if you’ll invest every month then it will be very difficult to calculate in this way. So, if you want to calculate manually in this so the formula for the future value of the annuity is annuity multiplied by raised to the power n, minus 1 divided by r This r is your rate of return or the interest rate A is the monthly or the annual payment, like in this case the annual payment is of 10,000. This is the annual payment of 10,000. So if we calculate the future value using this formula, in this case, so you will write 10,000 here,

And here you’ll write 1+ 0.07 since the rate is 0.07 raised to the power 3 because n=3 and minus 1 divided by .07 Now when you’ll do the calculation, you can calculate using any simple calculator So its value will also be Rs.32,149. So you can calculate directly in this way. So now, the example which we had taken as I have talked to you in the introduction If suppose, you invest 10,000/month in an investment Let’s say you are 25 years old on today’s date and suppose you can get 15% returns annually. And let’s say you keep invested for 35 years. Then how much money you will get in retirement? We will do its calculation in Microsoft excel because you won’t be able to calculate easily using the formula also Still, let me tell you So this total amount will be 14 crores 67 lakhs… 31 thousand 802 rupees only. Now we will see its calculation in Microsoft excel.

We will see this calculation also that how this Rs.32,149 will be calculated in Microsoft excel Let’s quickly see how these calculations will be done in excel. Let’s see the assumptions first. The present value will be zero in this case. Because we haven’t invested any lumpsum money right here. Now annually we are investing Rs.10,000 Our payments will be 10,000 every year. Our interest rates are 7% as we’ve assumed the FD rate of 7%. After that, we invested the money for 3 years. Compounding is annual i.e. every year You’ll get the money according to the compound interest. After that, let’s see how the future value of the annuity is calculated. So you’ll press “=fv”.

As we’ve calculated the future value in the previous post, it’s the exact same formula. Now as it’s asking you for the inputs enter the inputs. The rate basically will be this. Here we’ve selected this cell of 7%. You can do the input also and enter straight 0.07 here. After comma and space, you’ll enter the time period here the time period will be of 3 years. I’ve selected this cell. After comma and space, you’ll enter the payments here. As you can see from this PMT, this is the annuity. So you’ll select this annuity here. But before that, put the minus sign, as I’ve told you in the previous post also. Because this payment is being done. Right? So the money is coming out from your account that’s why you’ll add the minus sign. And you’ll select this cell after that.

After that, since the present value is zero here, that’s why we’ll enter zero. We’ll close the bracket and then enter it. See, we are getting Rs.32,149 is the exact same figure that we’ve calculated from the formula, right? Now, if you invest Rs.10,000 per month so how much money will it be till retirement? As I’ve given you the example, if you are 25 years old If you invest Rs.10,000 every month. Let’s say you earn 15% returns annually. And you keep it invested for 35 years. you keep invested in that product. Then how much money can you make in 60 years?

Let’s calculate that! Now, in this case, compounding will be monthly. Because you are investing every month, right? So, according to the monthly compounding, Let’s see what will be the future value of an annuity. So here we will write “= fv”. You’ll enter the rate as 0.15. Divided by 12. Pay attention here. Here, we are dividing it by 12 because the compounding is monthly, right? After entering the comma and space, we will select the period. In the period also, we’ll have to multiply it by 12 because we are calculating it on a monthly basis. After entering comma and space we will enter annuity here. How much are our payments every month?

So here, after selecting minus, we selected 10,000 according to the cell. After that, I pressed the comma and entered the present value 0. Because I haven’t done any lumpsum payment. close the bracket and enter. See, we are getting the same value. You will get Rs.14,67,71,802 after 35 years when you’ll get retired. So, in this way, we calculate the future value of an annuity. Now in the next post, we’ll see if your cash flow varies every month then how will you calculate the future value? Like in this case, we were investing Rs.10,000 every month If suppose we change it every month for one month 10,000, for another 14,000, and for some another 15,000,

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