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A person wants to invest $16,000 for 2 years and is consideringtwo different investments. The first investment, a moneymarket fund, pays a guaranteed 5.1% interest ...

Question

A person wants to invest $16,000 for 2 years and is consideringtwo different investments. The first investment, a moneymarket fund, pays a guaranteed 5.1% interest compoundeddaily. The second investment, a treasury note, pays5.3% annual interest. Which investment pays the most interest overthe 2-year period?Select the correct choice below and, if necessary,fill in any answer box(es) to complete your choice.(Do not round until the final answer. Then round to the nearestcent as needed.)A.The marke

A person wants to invest $16,000 for 2 years and is considering two different investments. The first investment, a money market fund, pays a guaranteed 5.1% interest compounded daily. The second investment, a treasury note, pays 5.3% annual interest. Which investment pays the most interest over the 2-year period? Select the correct choice below and, if necessary, fill in any answer box(es) to complete your choice. (Do not round until the final answer. Then round to the nearest cent as needed.) A.The market fund is the better investment, since the market fund produces $Blank in interest, and the treasury note pays $ Blank in interest. B.Both the market fund and the treasury note produce the same interest with $Blank. C.The treasury note is the better investment, since the market fund produces $Blank in interest, and the treasury note pays $Blank in interest. 2. Find the compound amount and the amount of interest earned by the deposit below. $2,000 at 7.68% compounded continuously for 8 years. What is the compound amount? $Blank (Do not round until the final answer. Then round to the nearest cent.)



Answers

The amount of money $A$ in an account with an interest rate $r$ compounded annually is given by $$A=P(1+r)^{\prime}$$ where $P$ is the initial principal and $t$ is the number of years the money is invested. a. If a $\$ 10,000$ investment grows to $\$ 11,664$ after 2 yr, find the interest rate. b. If a $\$ 6000$ investment grows to $\$ 7392.60$ after 2 yr, find the interest rate. c. Jamal wants to invest $\$ 5000$. He wants the money to grow to at least $\$ 6500$ in 2 yr to cover the cost of his son's first year at college. What interest rate does Jamal need for his investment to grow to $\$ 6500$ in 2 yr? Round to the nearest hundredth of a percent.

Difference. So in this question we are given that there is a relation between the initial principle which is denoted by capital P their time in the number of years the money is invested as small t and the amount of money in the account with an interest rate are component annually has given it equals two p times of one place Our hold the power of T. So we are given this relations now in the first part, we are okay, so that can be easily found. Bye. Using this relation which is given so we will be doing the part A. So now we are given that $10,000 investment, which means that for the first part, a A equals capital equals two $10,000 and we are giving their capital p which is the Oh, okay, sorry. I'm sorry. So, in the question, we are given there the principal amount which is $10,000 which is invested. So therefore, capital P equals two $10,000 so P equals to $10,000. We are also given that it grows to 6 $11,064 so therefore equals two 6 11,064 dollars and we are given that the investment rose into the amount of money after interest surrounded in the time period of two years. So two years. So now we can proceed with the question by using the same relation which is given We can proceed and therefore yeah, 11. We can put those all substitute the values which is given in the given relation as 6 11,064 equals two 10,000 into one plus R or to the power of two. No, I have substituted given values into the relation which is given in the equals two one point 14 Therefore, the interest rates are would be equal to 0.14 This is the answer of the first part. Now we would move to the next part B no. So I would be changing the color two a green so that I'm doing the second part of the question where we are, given that if $6000 investment that grows to 3 $7092.6 after two years, we have to find the interest rates. So therefore we will take the principal amount of capital PS $6000 so it would be equal to $6000. And then the amount which it grows up to is 3 $7092.6 per capital. It would be 7392 $0.6. And the time in which this investment grows into is equal to two years. We are to find the interest rate smaller. So by using by substituting these values into the Cuban relations, I would obtain the relation as 79 2.6 equals two, 6000 times one plus odd whole spread. By solving this equation, I will obtain the value of Mr Minute. Okay, Okay. I think I've done a small mistake. So So the mistake that I had done is that this equation is wrong After solving this equation is correct when we substitute the values in the first party. But the final part that we would that we will obtain after solving the equation would be one place R equals two 1.8 So it is not 1.14 I beg your pardon once again. So it's equal to so just a minute. Therefore it is equal to 1.8 Therefore, the interest rate are for the first part would be 0.8 No, to the second question. So I would be again using green color. So to the second part of the same question, we would use this relation. And then once we solve it, we would get answers. One plus r equals two 1.14 Yeah. Okay. So I think that I have made a calculation mistake once again. Just a minute. Okay. Okay. So it will be 1% equal to 1.101 approximately. After rounding it off up to three decimal places. I would get it as zero point 101 for the second case. Now for the third case, So I would be using wild color. So see the third part, we are given that Jamal wants to invest $5000. He wants to invest money to grow. So says that he invests to grow to at least $6500 in two years to cover the cost of his sons was here at college. What interest does Obama need for his investment to grow to $6500? in two years. Okay, So we are to find what interests it is that if we are again, need to find a rate of interest. So we are given that the principal amount is equals two $5000 and the amount which he wants is a equals two $6500. And the time period, which is given is equal b equals two, two years. Now, I'm again substituting these values into the Given the question. So therefore, I would obtain 6000. Okay, 6500 equal to 5000 and two one plus odd. Hold squared. Now, after solving this equation, I would get test. One place, sir, equals true, 1.14 Therefore, our record is your point. Wonderful. So this is the answer. Thank you. I hope you like the video

Okay, We are here to help Caroline work through this complicated situation, starting with Part A. She's investing $19,400 for three years out of 4.2% interest rate, compounded monthly on because it's monthly and equals 12. So we're going to figure out the amount of interest you would earn. First, let's find the final balance using the equation. B equals P Times one plus R over in to the anti. Okay, well, substitute all of our values in their 19,400. And for our we're going to use 0.0 for two. We need to convert that percent to a decimal and for N. We're using 12 and we're raising it to the 12 times three, which is the 36th power. So let's see what we get for that. So the final balance there is $22,000 and 23 cents. Well, we want to know the interest, so we need to subtract the original principle from that amount to get the interest. So we're going to subtract 19,400 from that amount, and the interest is $2600.23 Okay. Now let's work on part B to figure out the amount of interest you would earn with the other CD. So the other CD is also compounded monthly. So in is still 12. Same interest rate, longer period of time. Okay, so we're substituting our numbers into the same formula and we have 19,400 times one plus 10.4 to over 12 raised to the 12 times 3.5, and we end up with $22,466 and 30 cents. Now that's the final balance, and we want to know the interest. So we're going to subtract the original $19,400 from that, and the interest would be $3066.30. Okay, now we're in part C, and some things have changed for Caroline, and now she's earning her 4.2% interest for the 1st 3 years. But then she's only earning 2% for the last five months, and we want to calculate the amount of interest she earns in those last five months. But we have to start by figuring out what she's starting with at the beginning of that time period. So we need to know how much money she had in her account at the end of three years. So let's use the formula B equals P 19,400 times one plus 0.4 to over 12 to the three times 12 to figure out how much she had in her account at the end of three years. And you know, that is exactly what we did for part a. Come to think of it, we got $22,000.23 so why not take advantage of that? Okay, so what's gonna happen then is for the last five months of the CD, she's going to be earning interest on that particular principle. So we're going to use that as our new value of P over here for the final part of the CD. So now we're going to have B equals $22,000.23 times one plus 10.2 because now she's only earning 2% divided by 12. And for how long? Well, she's doing this for five months, so that's 5/12 of a year times 12 times per year. So that's really just a next opponent of five. It's gonna be five compound ing's and let's calculate that amount. So the final mountain now final amount now is $22,184.18. Okay, so the question is, how much interest did she earn in those last five months? So we need to subtract from this amount the principal. So we need to take $22,184.18 and subtract $22,000.23 and we end up with $183.85. That's the amount of interest she earned in that last five month period. Now, in Part D, we want to know how much interest she earns altogether. So the 1st 3 years she earned $2600.23 and in the last five months she earned $183.85. Those were answers from Parts A and C, and if we add those together, we'll get the total interest. So over the 3.5 year period, she actually earned $2784.8 sense of interest. Now what happens in Part E is we have to subtract the penalty so she pays a $250 penalty for early withdrawal on her CD. So we're going to subtract this from the amount of interest. So we have $2784.8 sense of interest. We're going to subtract the $250. So the amount of interest she actually gets after subtracting the penalty is $2534.8. Okay, now, in part F, she's going to withdraw $12,000. And so let's figure out how much money shall have left. What will her balance be? So remember her principal was $19,400 and her interest minus for penalty, which we just found in the previous part was $2534 and eight cents. So altogether, the amount of money she has is $21,934.8. Now we need to subtract $12,000. She's going to withdraw that from for, uh, for school expenses and that leaves her with $9934.8. Okay, now we're on part G. Now. Three years and five months have gone by and remember that she has this CD for three years and six months. So there's still one more month to go, and she's going to make 2% interest during that month. So she's making 2% interest on her $9934.8 that remains in the CD. So let's figure out the balance. We would start with the principal $9934.8 and multiply it by one plus 10.0 to over 12 to the first, okay, just one month of interest. And that ends up giving us a balance of 9000 $950 and 64 cents. So that's the total. What amount of that is the interest we need to subtract the principal from that and we get the interest. So we take 9950 64 cents and subtract the principal 9934 and eight cents, and we end up with $16.56. That's the amount of interest she made during that final month. So for the next part, let's find her total interest for part for the entire 3.5 years. And this is part H. So remember, for the 1st 3 years, her interest waas $2600.23. Then for five months her interest waas $183 and 85 cents. Then, for the last month, her interest waas $16.56. So the total of those is $2800 and 64 cents. So the total interest she earned was that now that looks like it's better than the 3% or the three year CD, because the three year CD was $2600 of interest. This is $2800 of interest. But don't forget that she had to pay a $250 penalty. So the extra $200 an interest is wiped out by that $250 penalty, and she actually got last then $2600. If you think about it that way. So when all was said and done. If she had just invested in the three year CD, she wouldn't have had to pay the penalty and she would have been better off.

By seeing the question. Four points in the question A. B. C. D. Alert for the move for the 1st 1. Which is there first one. Do your friends. But mm General 35. B. Mhm. Like yes. $2000 and dressed, right. She noted by our Mhm. Just 13.5 and dying. I just denoted whitey six months. So let's move to the separation him and dressed to uh into T by and heard. Which is 2000. Sorry, there is into 2002 13 On five and 6. Right. And good. So A. Is Yeah, amount. He is principle. All right. And dress and Yeah, he is $2000. I is 1 35 and is people S. I. Which is equal to $2,000 less 1:35, which is 2135. Yeah. That uh solution. The first point which is a Let's move to the 2nd 1. We shall be okay. So N. B. Just again given yeah, principle. And the worst thing and dress tracked. Just you know about uh yes. 10% and time which is denoted party just to me. Yes. Oh, so let's move to the solution. Mhm. Come down, right. They want to be And plus. Uh huh. Cut into divided by handwork and record close and who here he is. Yeah. Principle. Mhm. Uh this right. And dressed and it's mm mm. Nothing but uh here's so equal to B. One plus then divided by and by three then a world too. Then tell the one last stand by And to break it closed. three is equal to 10,000 310. So I equal to a minus B. Which is I called to 13,310 than 1000 which is 3310 Areas I should appoint. B let's for the move to the point C. So and want to see it's saying that and dressed right? Yeah 1970 years. Yeah. Mhm. To do 19 81 which is 7.2%. 10%. Hello? I want one 5% and the last 14%. So let's calculate 21st Word in 1974- 1991. That would take an average. Yeah. For the average It takes 10.2 plus 10 plus 11.5 plus 14. Do what everybody for. But I have rich come to 10.67 5%. So here the solution of point C. Let's move to the last point just pointy mm Well and we for the power right? Yeah. Yeah $10,000. Mhm. What it says or just price which is than 1000 daughter and then market well and dress for that. 6.6%. But he uh and disease 90. So that's calculated the yard calculation of pure Yeah. For our value by the chance. Right. Mhm. Do you dare to play far value into to 60? Yeah. Mm mm. The blood did. But dems of thank you. Let you 30 into Yeah. 100. Okay. Oh yeah healed carried to far ready minus Then $1,000. Bye by value. Thanks to today 60 92 100. Uh here the day 40,000 And 6.6. Mhm. All right, 94 good answer is then 1001 16 fight. So here's the R 44 solution of four points. So I hope you better understand the whole solution for any further questions. Courage. I'm therefore thank you.

So while seeing the question looks for the move to the answer. So the first one is it just principle would just be investing amount Which is $2,000. And the second is interest read which is our Just 13.5%. And the 3rd 1 is time I just denoted by D. Which is six months. So here at simple interest. Yeah. We into our into T. Divided by 100 which is 2013.5 into 65 100. So here is amount is among therapy is french people. I is impressed And p. is equal to $2,000 And I. is $1.35. So equal to P. Plus I. Which is yeah, Equal to $2000 plus $1.35. Which is equal to $2,135. So here is the first one. Let's move to the 2nd 1. Yes be. So let's see here that brain Sippel B investing. I'm out, which is $10,000. The second is interest rate Just noted by our with just 10 and the 3rd 1 is time we're just equal to three years. So at compound red compound interest. So let's see here that equal to be bracket one plus are divided by 100 bracket clothes into end. So here we see that he is a principle and our is interest rate. And and if number of yes. So let's make the solution. So let's see here that okay equal to be bracket one plus 10 divided by 102 3. It is equal to 10,000 bracket one plus 10 divided by 102 3. Which is equal to 13,310. So I equal to a minus P. So I equal to 13,310. Sorry this is I so minus 10,000 equal to 3310. So where is the final answer? Of the 2nd 1. So let's move to the 3rd 1 which is see So let's see here that and dressed two interest read 1978 two 1981 which is 7.2%. 10%. 11.5%. And the last one is 14%. So here we go through the average. So the average is 7.2 plus 10 plus 11.5 Plus 14. divided by for the final answer is 10.675 percent. So Here is the final answer of the 3rd 1 which is sea. So let's move to the last one which is D. So let's see here that Far value equal to $10,000. So the purchase price Equal to $10,000. So the market interest rate is six 6.6%. Where here And that days is equal to 90. So here we calculate. So that yelled equal to why are value minus purchase price is divided by far value into 3 60 divided by terms of maturity. Yeah and two 100. So here is yelled equal to far value minus $10,000 divided by far value and two 3 60 by 90 in 200. So that he yelled is equal to. Mhm. Okay 40006.6 divided by 94. So the final answer is 10001 65. Okay so here's the final answer of daddy. So here is the oil. The four solutions of the question. I hope we can understand all the four point solution which are given the question. So for any further queries and doubts I am there for help. So thank you.


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