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[-73 Points]DETAILSROLFFN8 5A.038_MY NOTESASK YOUR TEACHERPRACTICE ANOTHERmechanic bartows 59500- expand hls garage. The Interest rate Is 10%, compounded quarterly ...

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[-73 Points]DETAILSROLFFN8 5A.038_MY NOTESASK YOUR TEACHERPRACTICE ANOTHERmechanic bartows 59500- expand hls garage. The Interest rate Is 10%, compounded quarterly with payments due every quarter: What are the quarterly pavments the Ioun to be pald ff In vears? (Round your Iinal answer to tVo declmal placesAuTo SkPAdditional MaletiniyEBook

[-73 Points] DETAILS ROLFFN8 5A.038_ MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER mechanic bartows 59500- expand hls garage. The Interest rate Is 10%, compounded quarterly with payments due every quarter: What are the quarterly pavments the Ioun to be pald ff In vears? (Round your Iinal answer to tVo declmal places AuTo SkP Additional Maletiniy EBook



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Give the local linearization for the monthly car-loan payment function at each of the points investigated in Problem 35 on page 747

So in this problem we're told that a credit card is going to charge 15.3% interest and it's going to be compounded monthly. We're being asked to find the effective rate of interest. Okay well if you think back we have a formula to do this, here's what it looks like. It's one plus I divided by n. This whole quantity is raised to the end power and then we're gonna -1. I represents our interest rate which will have to be made into a decimal and and represents the number of times it's getting compounded. Okay well we'll have everything that we need So because our interest rate was 15.3%. If we were to make that into a decimal point we need to move the decimal to place to the left. So this would be 0.153. And because it's getting compounded monthly there's 12 months in the year so far in value with equal to 12. So now we're gonna substitute these values into our formula. So we're gonna have one plus 0.153 divided by 12. All raised to the 12 power and then we're going to subtract one. And this is something you can punch in your calculator all at once. And what you find is that you'll get a value of 0.1642. Now that doesn't mean that 0.1642%. This is our percent value as a decimal. So now we have to turn it back into a percent. So remember how before we moved up two places to the left to turn it back into a percent. We're going to move our decimal 20.2 places to the right. So if we go 12 That means we'll have 16 for 16.42%. So that would be our effective rate of interest.

In this question we're asked to compare the return, compare the compounding effect status, monthly compounding effect and the country's comporting effect that we discussed in problems number 1 to 6. So in problems number 1 to 6 we took you know three different values that is in one and two we took $500 to in three and four we took $1000 and in 45 and six it was $5000. And we took the different cases of continuous company a monthly combating using the same interest rate. So Here I tablet returns at the end of 15 and 35th year when you do a monthly committing anyone in this community. So it's like in the case of monthly commuting and discovering at the end of 50 or you know the returns are almost same. I mean there is nothing to me it's the same like there is no difference actually it's it's it's the cases seem like almost in the all the, all the three cases here are, the only difference is like You know uh just half a dollar or something. That's the only difference you can see here even in the case of $5,000 when it comes to 35 years when it comes to 30 days also and there's a 500, it's really close like there is no big difference, there is no difference And these are $1,000 also. There is no difference like but it was the same When it comes to $5,000. We can see a kind of you Compared to all the other values, there is a difference of around like $7 something. So there is, this is the only case we can see a difference when it comes to monthly company and condoms converting. So actually this question the workers have to, you students like you have to do different calculations and find out if there are any, if there is any dramatic difference between these two. So what I'll lose that I just, you know, these two other families that is his body can't uh sorry, monthly uh this for the, you know, competing interests normal converting case that is monthly commuting daily compounding, uh, only converting. But this is the continent's company question. So the rate rate of interest will be the same. But we can, you know, uh, here we all the interest rate that up very less. Like I'm not very less. But uh, according to you know banking banking centers that will be Okay like three persons or something. But let's say we go with an account, let's say we are investing, let's say we're investing $5,000. Really $5,000 at the rate of 8% per annum. Great person planning is the interest rate and we'll find the difference between monthly comforting and continues company. Okay, so that's what we'll do in this question. So I'll just do this example for you and what you can do is that you can just uh play with the values that is the total amount the tenure of investment, the interest rate and then find a fine. If there is any like major difference between monthly company independence company. So what we can do here is that she is you know, I'll just go this way itself. Like If you have $5,000 and eight personal interest when it is monthly common country single product. What will be the returns at the end of 15 and 35th is what we're going to do. So let's start with monthly Good morning. First the question is the question will be a soft is equal to F. D. is equal to 5000 multiplied by one plus. Are buying us eight persons right? R. Is equal to I'd like to hear. How does he do? 8%. Is that is 0.08 mm N is equal to write monthly compounding. So the question will be 0.8 divided by 12 12. T. This will be the question right for monthly company now, A F five is what we need to see first. L five years 5000 multiplied by one plus 0.08 Divided by 12 to be bought of 12 multiplied by five. Right? A little bit returns for five years. On calculating it will get one plus 35,000 molecular one plus .08 divided by 12 to be got off 12 multiplied by five. That means returns at the end of 5th year. We meet 7449 23. This will be the returns for the at the end of 5th year. At the end of 35th year I have 35 is equal to 5000 multiplied by one plus 0108 divided by 12. Tomorrow 12 multiplied by 35. Right now, let's see the final month. That is 162,000 400 81,400 and uh 62 point 75. This is the amount that we can expect at the end of 35 years. Okay, this is the amount that we can expect at the end of 30 days you started with 5000. Okay so uh and you have $81,462.75 at the end of 35 years when the interest returned? Raters 8% is okay. Now let's go to the monthly continues compartment case. So it's got the content is so important case. So that is the question will be a F. T. Is equal to 5000. This will be the equation very that is if this will be it for the party That means 5000 multiplied by E. To the goal of RT. That is 0.8 T from the equation now for 50 years and the atmosphere F five is equal to 5000 multiplied by each member of the ribbons. Rate multiplied by. That's true. So high. Uh Fight you also. Yeah. So that means on calle fashion will get 5000 multiplied by E. To the power of 0.08 multiplied by five. And the returns is 7459 12 Mm. Yeah. To returns at the end of fifth year you have 35 years. 5000 multiplied by eight without a 0.08 multiplied by 35. This will be mm 82,000. There was 223 uh This month will be written at the end of the 35th year. Okay, so now compare the values, I just write it here. So it started with we have $5,000. Then in the case of uh at the end of 50 or three in the index of continents company and in the case of monthly combat and this is what what we need to, you know, save difference. So when it comes to The end of 50 year and the end of 35th year, So this is the country's good morning is right. So that means at the end of 5th year we have 7400 and 7459.12. That's what you get at the end of 31 year you get 82,223.23. When you go to monthly comedy, you've got 7449.23 7449.23. And at the end of 5th 30th here you get 81,460- 81,462. Find 75. This is what you get to see the difference here here. Also here also like like 8% which is considered to be uh the interest is considered to be on the higher side given then the difference is like How it's it's around you know $800 or something right? Yeah $800 or something in 35 years. When it comes just five years the difference is like $10. So see the uh thing here like even the difference between continues convenient monthly co morning is it's not that great actually. When you compare when you compare like yearly compounding, when you come back nearly component with n. Is equal to one and these two continues company then you won't be able to see a larger difference. But when it comes to when the frequency of computing increases, you don't see that much of an increase in the returns. So if you want you can try with different examples and do the computation and tablet this and so that you can understand the whole concept. So I guess this is enough for this restoration you have yourself so once again here the whatever did here is that from the christians want to exercise established the returns when it comes to a somebody For 15 and 35th year. And so that there is not much of any difference when it comes to returns. So I just took one another example where we are investing $5,000 that tend to serve a person is and for the same like five years and 35 years. So calculated the returns according to both the cases and found out that be and the friends is only I would say like I don't think, you know, there's only 1% of the total amount that you get. So yeah, considerable amount of written something you can consider is the difference that you can consider. You're getting that only when you're investing for such a long time with a good interest rate for this money amount. Okay, so the amount if you go for like 50,000 or something, then yeah, then you will be able to get more returns. Okay, So you just have to do the calculation and then you will understand that. So, so that's it for this question. So, I hope you understand the concept by

Hello. Hi here in this question we have to solve any question given its minus seven. The old power three by five is equal to eight. We need to solve this so you can see there are there's a fraction on the our 51 where every year. So first we take this hour one by five into other side we get our five april five value. We can find out we get 32,768. Next to we like cube root on both sides. At least 7 32,068. For our one day when you take your group will be getting answer 13 to him. No it is very easy to solve that. Seven will take into right and seven we get 32 plus seven that is equal to 39. This will be the required answer. I hope this answer your question. Thank you.

Alright in this problem we're going to see uh at what rate you need um to grow $16,000 into $20,000. If it's compounded quarterly over 7.25 years. So I already laid out the information R. P. In this case is our principle is $16,000. We're solving for a rate. That's what we're looking for because it's saying it's compounded quarterly and not continuously. Um We're going to use the A. Equals P times the one plus our over N. To the N. T. Formula. Alright. We're not using P. E. R. T. Um You use that one? It says continuously. Okay. Uh So because because I know I'm using this formula, what I'm going to do is start plugging in my values. All right. We want to see when this account or at what rate the account needs to uh Be at to get to 20008. So is my 20,000. We already said that P. is 16,000. All right. One plus the rate which we don't know. We're solving for our over end quarterly means four different periods to the N. T. So for Times the time which is 7.25. All right. I'm going to do kind of two moves in one. Um And I do this in my calculator. I don't a lot of this in my calculator, but I'm not going to switch tabs. All right. So the first thing I would do is I'm trying to get my are by itself. So I'm going to divide away this 16,000 to the other side. All right. 20,000 divided by 16,000 is 1.25. All right. Now this is helpful because I'm I'm pretty much isolated. Um Not all the way, but I'm getting close. Okay. So I still have one plus are over four And I can do that Math four times 7.25. That's 29. All right. So, I have uh parentheses raised to a power. I can get rid of that power by taking that route to both sides. So, my next step is to take the 29th route of both sides. Because that will cancel out the exponents for me. All right. The 29th route of 1.25 that I do in my calculator comes out to be 1.00772. I did plenty of decimals because we don't want to round too much in our intermediate steps. All right. Now, I got rid of that exponents. So I just have one plus are over four on this side. All right. So, if I want to isolate the r the next thing I'm going to do is subtract one to both sides. Okay, so I get rid of this one. Uh and then this will come out to equal zero 0772 is equal to our over four. Well, because our is being divided by far the way that I want to undo that division is with multiplication. So I'm going to multiply both sides by four. All right. And four times the .0077 to um comes out to be um point zero three 088. All right. Um Now that's our rate. We want to express this as a percentage, so we're going to move the decimal over twice. All right. And then um if we wanted to round it to the nearest 100th for a percent, we would say 3.09 percent and that would be our rate.


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