And this question we're talking about comporting interests where interest is being given on the interest that has already given for the principal amount. Okay. And in this question compounding is done every month. Okay. For a principal amount of for a principal amount of $5,000 at a rate off at a rate of 2.125% days. Just 2.12 5000 days. Now uh we told that the component is done continuously. That means number of compounding in a period is in in nine years 12 right if it is being done abdomen that 12 times in the land. And the equation that mean it uses a F. T. Is equal to be multiplied by 1 to 11 plus R. By holding the bottle anything. T. Is a number of years for its the particular investment is kept in the account and pc principal amount that has been invested in that. I can't R. Is the rate of interest which has to be extras in terms of the numbers or not in not in terms of percentages and nz number of compounding is done in a year. Well A. F. D. Is the amount that you can expect for the account. A hole at the end of two years. Okay So the pencil owned are and but here are we should not take it in person. This that means we have two divided by 300. So that means the robot and 0-1 to fight. Is the amount that you take is the value that you need to use. So the first question is two to express the amount Indeed in this particular account in terms of T. So you have to do is that you just have to substitute these values into formula. And very big wish. So that means A. F. T. Is equal to P. That is 5000. uh by by one plus R. C. 010 to 1 to five divided by 12 Under Barak 12 T. Okay so this is the formula that problem. This would account Coming to the 2nd question. That is how much will be the amount that is that we present in this political economy at the end of at the end of 50 year, 10 p.m. 30th year and 30 50. So all you have to do that you have substitute T. In this formula and find the answer. So that means air fight. The first 150th is 5000 multiplied by one plus 3.0 to 1 to five Divided by 12. Tomorrow. 12 multiplied by five. So that means calculating that will get 5000 multiplied by one plus. Find 0-1-5 divided by 12. Hold the bottle 12 multiplied by five. Right? We'll do that. We'll get 5500 And 59. 5159.98. The Smiths will be the amount That they can hold at the end of 50 At the end of 10th year. The end of 10 years At the end of 10 years is equal to 5000 multiplied by one plus 010 to 1 to five Divided by 12 or to the core of 12 multiplied bite and that means it will be 6000 6182.67. Especially with the amount they can we hold at the end of 10 years now coming to 30 years. F 30 is equal to 5000 Multiplied bike, one plus 0.02125 divided by 12 3, 12 multiplied by 30 is equal to 9009453 Point three. Uh Yeah for rounding it off you get mm for that. Okay so that's it and that means f 40 if you want to be precisely 40. Uh F 35 is equal to 5000 multiplied by one plus 0.2125 divided by 12 at risk To the bottom to grab it 35 and he will get 10,000 10,000 512.13. Okay, not one actually will get one for Yeah you get one for yeah so just a minute. Yeah we'll get one for because you are asked to round off the answers to its nearest center so that's how we get one for uh white, you will get one thing anyway, be careful about the rounding of rules. So this is how to make sure that it is correct. Okay okay So uh this is actually the amount percentage vehicle at the end of 50 year will have 5,559.98. And at the end of 10 people have 6,182.67. At the end of 30th year we'll have 9,453.4. And at the age of 35th year we'll have 10,512.13 dollars. That means my 30th year the money has already doubled. That brings us to the 3rd question. That is we need to find the number of years that will take for the amount for the amount to become double matters. If the principal amount was What do you want us 5000 Then the amount at the end of two years has to be 10,000. So you need to know how much it will take. You know that by 34 years it has already doubled. But we just need to do the calculation to know how much to take. So subscribing the virus will get 10,000 subscribers virus today to this equation. Okay you need to subscribe violence in this equation and you need to find T 10,000 is equal to 5000 multiplied by one plus 010 to one to fight divided by 12 by 12 To about 12 T this is what we need to find out is what we need to find. And dividing both sides by 5000 wickets. To strip one plus 0.0 2125 x 12 To be part of 12. T. is equal to two playing log. You can apply a natural logarithms or uh Common love with anything can be applied in a problem. So applying I'm using as an algorithm. Natural logo one plus 0.02125 divided by 12. Or will use common just for this case. Okay so it doesn't matter actually. It doesn't change anything much but I'm just you can use any base if you want. If you have a calculator that supports different base then you can use for example you can use base too. The right hand side becomes one. No problem. Uh It's just that uh you can try using natural uncommonly with them but when it comes to e you can you have you can't use that slogan because it's simpler when it comes to 10. Use common law given because it makes things simpler. I think we'll do love to. That means playing properties of longer than we get 12 t. multiplied by log off. And save the black. It will help one plus Find 0: 1- five divided by 12. That is one one point we have a let's take the long term. I think that would be better because if we just round off here will have it's really a bit difficult log of that particular value is seven points 7.68 multiplied by 10 to the -4 is what we get is equal to log to. Okay so that means 12 T. is equal to T. Is equal to T. Is equal to Yeah. Long two divided by 12 multiplied by 7.68 multi private. And the world -4 which on you know dividing will get 12 Very boy 7.68 and grab it into a lot of -4. When you do that you'll get 32 points right? 30.66 years. That means it will take 33 years For the investment to double that is from 5000 to 10,000. So here uh What happened was in my 35th year it became on 10005 and told but by 33 years itself It has reached $10,000. So now do they finally question that is. And the final one where you have to find is that you need to find the rate of change of the amount at the end of fourth quarter of the year and then find the rate of change of amount At the end of 30 40 or 2 35th year. And you need to compare this to compare this to Rates. So that means we might find the amount at the end of for Pier 50 30 40 858. Right? So then the fourth year you have to use the formula that is 5,000 1000 Yeah 5000 Multiplied by one plus 0.02125 Divided by five, divided by five divided by 12. Yeah, By 12-12 multiplied by for this is what we need to find. Right? So that means by 1000 multiply it by one plus 10.0 to 1 to five divided by 12 to the body off 12 multiplied by four is equal to 5443 points 18 responsibly. The agenda for pia. Now I am five am are at the end of 50 years And then the 50 we already found out right there is 5559.98 5559 198 At the end of 50 will help at the end of the 34th year will help At the end of 34 there will help. 10,000 Sorry, I joined the calculation first 5000 multiplied by one plus sort of 10 to 1 to five divided by 12 or 12 multiplied by 34. That will be 10291 Point Yeah, fine please. This video is good enough. 30 40 Coming to 35th year. We don't need to calculate it again because we already found out. Right, That is 10,512.13, 10,000 final and 12.13 This motion video going to end up Dennis 30 15 Now to Calvin the rate from 48 to 50 year. What that means And more than 10 to 15 minutes I'm going to be enough for people to buy for one slide. Right? So that means 5500 and 59. Find 9 8 -5000 Foreign Land. 43 points when it divided bike. Hi my passport. That's what we need to find. Mhm 5159.98 -5443.18 You were by one is equal to 116.8. That means since it's the rate of six from 48 to 50 year when it comes to 34th year to 35th year will help 10512.13 10,000- 91. Yeah, find the right way Prime Minister before that is 10512.13 10,000 to 91.3. So little help Do 20.8 Quick. That means the amount of change of the rate of change from 4 30 to 50 years. 116 $100. Why demonstrators things from 34 30 35 theaters to 20.83 which means Almost more power more than a difference of 80% taste right? It means the rate of change in a compounding interest case and Emily is not the thing. It also varies but that when they're more description they're going for more number of years. This rate of things will also be higher. For example like 50 58 year old, 51st year will be different. Higher Landers. Okay, so one second through the steps. So we have uh, the problem we're compounding interest is considered, you know, I'm comforting is done every month. And for that the question we have to use is this so they're generally so the question that represents is portable account will get it by substituting the values that were given To the general formula we all this with help of that. We're able to find the remote at the end of fifth year, at the end of 10 Pierre at the end of 30 theatre and at the end of 35th. Yeah, this is ST look at one thing mm just yeah Uh, the next one you are asked to find the time it will take in years to find the signs are that the amount will become double and that of the investment amount. So doing the illusion, we found out that It will take at least 33 years or in 33 years the month and the economy will be doubled. And finally we are asked to find the right person from 14 to 24 to 34 year. We did that, and in comparison, encountered that The rate of things from 30 for 30 series, like the matter for 250, hope you understood this.