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Kumar and in this video. We will understand the basic concepts of energies present value value the. Question here is how much do you need to invest.

Now at 48. Provide regular payments of dollar 500 per year for the next four years now. When we are talking about how much do we need to invest now theyre interested in present value.

So that word relates to the present value so the key word. Which helps you to figure out whether it is future value or present value correct. So you have to identify these words.

So. That you can apply the correct formula right now. Lets look into the question.

Draw a timeline and understand how to solve it says how much do you need to invest now at 48. To provide regular payments of 500 per year for the next four years. So.

Let me show. A try and timeline here for four years. So we will say now is at present.

Well call it zero and these are our years. One two three and four right so after one year. So to provide regular paper.

So 500 per year for the next four years so after at the end of the year you can see next year. One two three four right so and how much do we need we need regular payment of 500. And the question is how much do we invest now right so invest now means we need to find their present value.

So. What is this present value of this 500. This is what we need to figure out what is the present value of the 500 which will get after two years.

What is the present value of 500 which we are going to get after three years. And what is the present value of the last 500 which we should be getting after four years. So that is what we want to figure out this is this is what we are saying is his present value right sum of all this when you add them up when you add them up then you get your also so that is the amount which you will be investing correctly now to help you figure out how to calculate this lets remind of compound compounding formula.

So amount a. Ill just derive. It here e is the amount and p.

Is the principle invested which we are saying present value is the future value and if you invest it then if the rate of interest is are let me write i in this case. We are doing per annum. So like the purpose of taking this per annum is not to confuse you with the compounding period.

So we have kept compounding period. As one just to make it very very simple right so n. Is also equals to number of years since the compounding period is one year and from this formula.

If you want to rearrange 4p. What do you get a divided by 1 plus. I to the power of n correct.

So so. The principal amount is equals to a divided by 1 plus. I to the power of n right so now in entities.

We talked about present and future value scraped. So so we say p is so you can replace this with pv for example right so you get the present value of all these amounts. Which you are going to get after a year two year three year or four years so applying this formula.

We can find the present value of each 500 correct. So we can say that this value here will be is 500 which you get after for one year at present. If you invest 500 divided by one plus rate.

Of interest let me. Write down here i. Is.

48 right. 48 that really. Means 0048 right in decimals divided by hundred so it is one plus 004.

8 to the power of one because it has invested for one year for the next. One it is going to be 500 divided by one plus 004. 8 2.

Likewise these are the present values for each okay. I can also add and write down right so one point zero four eight 4 fine. So these are the present values you can use the calculator to calculate these values so well do five hundred divided by one point zero four eight equals two in decimals.

We can write this as equal to four seventy seven. So youll round them to two decimal places for seventy seven point one zero right the next. One is five hundred divided by one point zero four h square.

So that gives you four fifty five point two five and then we have five hundred divided by one point zero four eight cube and that is four thirty four point four zero. Were just rounding them to do decimal places. Five hundred divided by one point zero four e to the power of four equals to four one four point five zero right you can see that their present values are kind of decreasing because that money after four years will compound to five hundred so it makes sense.

So your calculations are correct. Now you can add all these so well add four seventy seven point one zero plus four fifty five point two five plus four thirty four point four zero plus four one four point five zero equals two in decimals. We get this amount as one seven eight one point two five right so thats the total amount which well be investing now correct.

So this is the amount which we invest now and what do we get out of it we get five hundred each year for four coming years. So that is what it is so you can actually plan sometimes for example a study loan so that you know when you invest as much you get enough money to pay off for you to ship for example. So that is how it works now another way to calculate this was to use the formula directly.

So thats the formula or which is combination of what we did with geometric series formula right so. Let me give you the geometric series formula. Which you might use to calculate geometric series.

Is sum of n. Terms. Is equal to a times.

R. To the power of n. Minus.

1. Divided by r minus. 1.

Now. In this particular case. What is a so a is this amount five hundred divided by one plus zero point zero.

So i could write e is equal to five hundred times. One point zero four e to the power of minus. One correct or you could write it as it is and r in this case is youre always multiplying by one over this term right one over this term.

So itd be one point zero four eight to the power of minus 1. And n. In this case is fool for you so you can also use this formula.

Find e r n. Substitute. These values and calculate so you can do this as an exercise you will get the same result.

Now you can also use the combination of these will give you a simplified formula for present value where this present value is the regular amounts you get times. One minus. One plus side four minus n.

And everything divided by i so we can use this formula and calculate so so let me again do the calculations using this formula correct. So what we have here is a say present value is equals to. Rs500 we have 1 minus 1.

Plus 004. 8 to the power of minus. 4 since 4 years divided by i.

Watches. 0048 right so so thats the formula. Lets apply the formula and check the result.

So what we have here is 500 within brackets 1 minus within. Brackets i can write this as. 1 okay plus 004.

8. Bracket close to the power of minus 4. So let me write this in brackets.

I should use the other actually let me delete this okay. So i should use this. Right.

4 bracket close again a bracket close divided by 004. 8. And that gives us 1 7.

8. 1. Point 2 4.

So we get 1 7. 8. 1.

Point. 2 4. 3.

Anyway. So it is kind of accurate. What we did why this was rounding every time so we are rounding at the end so the present value so we can write on our answer.

In dollars. The present value is 1 7. 8.

1. Point 2 4. Right so that is how you can actually solve this question so in this video.

I have given you options and i hope you understand how to solve such questions. Im. Adele kumar.

You can always share and subscribe my videos. Thank you and all the best .

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