in-2000-jennifer-invested-1000-in-a-seven-year-certificate-of-deposit-mathrmcd-that-paid-2-interestc

Question

In $2000,$ Jennifer invested $\$ 1,000$ in a seven-year Certificate of Deposit $(\mathrm{CD})$ that paid 2$\%$ interest,compounded annually. When that CD matured in
$2007,$ she invested all of the money in another seven-year $\mathrm{CD},$ also paying 2$\%$ compounded annually, that matured in $2014 .$ To the nearest dollar, how much
more money did Jennifer earn from 2007 to 2014 than she did from 2000 to 2007$?$
$$\begin{array}{l}{	ext { (A) } \ 22} \ {	ext { (B) } \ 44} \ {	ext { (C) } \ 149} \ {	ext { (D) } \ 171}\end{array}$$

Lily An · Accepted Answer

Okay, so this one says. In two thousand, Jennifer invested one thousand dollars in a seven year certificate of deposit, which is a CD that paid two percent interest, compounded annually. When that CD matured in two thousand seven, she invested all of the money in another seven years CD, also paying two percent compounded annually that matured in twenty forty to the nearest dollar. How much more money to Jennifer earned from twin two thousand seven to two thousand fourteen? Then she did from two thousand to two thousand Son. So currently, we know that the question says we&#x27;re comparing from two thousand seven to two thousand fourteen and twenty two thousand to two thousand seven. So let&#x27;s go ahead and write those out. So we have two thousand two two thousand seven. Then we have two thousand seven two two thousand fourteen. So let&#x27;s go talk about the Saturday equation. So we know that the equation says that X, which is the final amount, is equal to the eye, which is an initial amount up times one plus the rate razed to the T power. So let&#x27;s go ahead and do that for the first situation, which is from two thousand to two thousand seven. So we know that in two thousand she started with one thousand dollars and then it was a two percent interest so that we can say one plus zero point zero two because that&#x27;s two percent in decimals on then. If we went from two thousand to two thousand seven, that&#x27;s seven years, so we can raise that to the seventh Power. If we do that, we get one thousand one hundred forty eight point six nine. So then that means that she earned whatever difference from this to one thousand would be. And if we subtract this one thousand from this figure that we just got, we should get the amount of money that she actually earned. Over those seven years, we&#x27;re just going to be one hundred and forty eight dollars and sixty nine cents. So that&#x27;s how much she earned from two thousand to two thousand seven. So then must calculate the final amount from two thousand seven to two thousand fourteen. So we know that in two thousand seven she started with this amount of money because she that&#x27;s when the CD matured for the first situation that she took that same a lot of money and put it in a different city. So then we can say that that&#x27;s our initial amount now and then we know that the rate is going to be the same because also two percent and then again in two thousand seven to two thousand fourteen is another seven years. So then we conclude that into our calculator on DH. Then we should get one thousand three hundred nineteen point for eight. So then again, if we subtract this final amount from our initial amount here, the one three one nine point four eight minus the one one for eight point six nine, we should not be able to find out how much money she earned between the years of two thousand seven and two thousand fourteen. So if we subtract that, we would get one hundred and seventy point seven nine. So then we&#x27;re not done here because this is the amount of money that she earned from two thousand seven to two thousand fourteen. But the questions specifically asks how Muchmore money Jennifer earned from this second period. Then she did from two thousand to two thousand seven. So then we have to stoop. Subtract the final amounts earned from two thousand seventeen to two thousand fourteen and this figure right here, which is the two thousand to two thousand seven, so that if we do one seventy point seven nine minus the one forty eight point six nine one, forty eight six nine and we should be able to get twenty two point one. So then we know that twenty two dollars is the difference. So Jennifer made twenty two more dollars in the second scenario from the second CD, as opposed to the first CD.

Yousef Sheikh · Answer

Elissa opened a retirement account with 7.25% a PR in the year 2000 and her deposit was $13,500. And then how much was he? How much will the accountant be worth in 2025 if the interest compounds monthly? And how much more? Which you&#x27;ve made an interest if she compounded continuously instead. Okay, so we basically have two use the same equation as before. So it&#x27;s going to be, uh, let&#x27;s say it&#x27;s gonna be hey, is the final amount peas. Initial times of one plus are, which is a PR over compound number to the N. T. Now we have her initial deposit is being 13 13,500. Uh, the P r a. 7.25% monthly compounded monthly. So that means it would be 12 because there&#x27;s 12 months in a year and we do it by years. And the time would be 2000 to 2025 25 years basically, and we&#x27;re trying to find the final amount. So yeah, we have everything. So pray so pretty straightforward. Equation on. The second part&#x27;s gonna be losing more tricky because we have to do it come continuously. And we have to see the difference between the two. Essentially, to see how much more money she would have made if she had done continuously. Not Buckley. So let&#x27;s do this question for so s O. We have 13 500 times one plus member speak. Desperate forms of 07 25 take a 7.25%. Same thing Divide by 12 because 12 times per year gives monthly and then time or to the 12 times 25 25 years power. And then we just do some math and we&#x27;re going to get the final answer, as did my calculator. But quickly, one closer, 10.725 divided by 12 to the 12 times 25 power, and we&#x27;re left with 82,000 $247.78. So, listen, being banker now, using just a retirement fund with the initial deposit, only 13,500. So pretty good. Um, so I should be going actually round it to 48. Probably if you only want, uh, you know, dollars. You don&#x27;t have to do with sense if you don&#x27;t want to. But it&#x27;s gonna be this around this amount. And now we have to do the second part, which is how much more which you have made. If it was compounded continuously. So we&#x27;re gonna put the exact same equation. 13 500 put times one plus 0.725 over. And we&#x27;ll have a second times or to the something power. Times 25. Everything&#x27;s the same, except for the compound continuously. All right, so what exactly would that be? S. So let me make sure the first part was actually right. I don&#x27;t wanna do this first part of the second part of them. Figure out that that was wrong too. So, yeah, this is right. Um, now, let&#x27;s see. It&#x27;s so let&#x27;s take a look at the second part. So we want to do the exact same thing, except it&#x27;s compounded continuously. Now, one thing to note is we. There&#x27;s a difference between being compounded continuously and being compounded by a real number. If it was compounded annually, you would do one semiannually be to monthly B 12 daily, 3 65 What do you do with its continuous actually um, now there&#x27;s a way to do it our way to think of it logically, right? If you have, you know, legendary formula. Where it&#x27;s p times one plus, let&#x27;s say it&#x27;s a some rate over and times into the tea. And then if it&#x27;s continuous, that means and is basically a huge number. It&#x27;s Infinity&#x27;s like every second, every millisecond and is approaching affinity basically. And then we have this scenario right here. It&#x27;s the answer is not gonna be, um, in this form, the new formula. Actually, it&#x27;s going to be a different way of writing. It is a different formula that we use for, uh, I can&#x27;t go any interest, combat it continuously, which is actually going to be key times e to the Arctic p Times E to the rt. And the reason why this is, uh, the new equation for a compound in continuous interest is because as engrossed infinity, there&#x27;s a whole like formula and whole like proof for that. Basically, this is gonna become really big. And then it&#x27;s actually gonna approach this part right over here is going to approach E and so is actually gonna pee Times E. And then our and then t you&#x27;re gonna be over there by itself. There&#x27;s a whole, like, Wait till I show you. But I won&#x27;t do it for this problem. Just know that when we&#x27;re doing with, uh, director to when we&#x27;re doing with compound continuously, we&#x27;re gonna use this formula instead. Not this formula. So let&#x27;s actually get it. Um, let&#x27;s use. So it&#x27;s going to be 13 500 times e to the rt, so it&#x27;s gonna be a 0.725 times 25. So this is basically the same. We could basically scratch this equation. You don&#x27;t even need this. So, so far we have this number, and then we&#x27;re gonna basically calculate the next number right over here, Which is gonna be, um, let&#x27;s see how he&#x27;s my calculator again. That&#x27;s going to be $82,697.60 three cents and actually all go back to writing this and, um, does more form to with sense, because we&#x27;re gonna have to use it for, uh, the next part. But I don&#x27;t have the exact number. Not like next month, yet you can estimate at the end, So we have two numbers so far. We have the first part when it was calm, pounded monthly, and we have the partners compounded continuously. Now, if you want to see how much more money Elissa would have made if she comes out of continuously verses monthly, you literally just attracted to you. So it&#x27;s going to be, uh, this one right here, so I&#x27;ll put you see, for continuous minus this one right over here, which is em for monthly. And we have to track them and we&#x27;re going to get $449. My four little nine. Sorry. $449.75. This should be your answer for the difference between the two calculations for monthly and continuous rate.

Lily An · Answer

And so for looking to see how much more money to Shawn&#x27;s initial deposit will have earned, then Jessica&#x27;s We first have to find the amount for their final that so to Shawn&#x27;s final remount, and we want to subtract Jessica&#x27;s final amount. So first of all, it&#x27;s going to find to Shawn&#x27;s final now, and we know that could be ah, found by the equation one hundred, because that&#x27;s the initial amount on then one plus the rate which the rate it says it&#x27;s two point five percent. So two point five percent express of the decimal. It&#x27;s your point zero to five to the time, which we know is going to be ten years. And then Jessica&#x27;s Final Mount is just gonna be the same one hundred dollar initial deposit. But then we know that her rate is only two percent, so it&#x27;s going to be your points. You&#x27;re two faced the same amount of time. Ten. So then way do that. That&#x27;s going to be so the left side. If we do that, it&#x27;s going to be one hundred and twenty eight dollars and one cent. And then for the right side for Jessica&#x27;s amount, you know that&#x27;s going to be one hundred and twenty one dollars and ninety cents. So if we subtract them, I get six dollars and eleven cents. So then that means that this is a difference between her Shawn&#x27;s initial deposits, earnings as a procedure. Jessica&#x27;s initial deposit. Ernie&#x27;s after ten years. So we know we consider it up like that. Just a circle back, because our equation is gonna be final. Siegel to initial again times one plus the rate expressed as he does, long razed to the time.

Ankit Gupta · Answer

in the question. Let&#x27;s assume that the amount X is invested at the rate off 4.5% or we can say 0.0 for five. Okay. And the remaining amount that will be 12,000 minus X that will be invested at the raid off 4% or 0.4 Okay, so let&#x27;s can play dying dressed, then intrest for a year will be amount that is X rate 0.45 time. This is one amount 12th will be 12,000 minus X in does 0.4 multiplied by one and this interest is equals to 5 25 It is given in the question, so this will be 0.45 x plus. This will be for 80 minus 0.4 x. So this goes here. It will become 45 5 25 minus 4 80 when 45 0.45 minus 0.4 We will get 0.5 x Then we can say X Is it cool? Stow 45 divided by zero point double zero fight. So we can say X is 9000. That means amount invested in 4.5% is $9000 and 4% will be remaining that this $3000. So this is that so.

Amy Jiang · Answer

Okay, so we&#x27;re given. We&#x27;re ask defying the present all your given that we have some compound amounts. So we have an equation for that. That&#x27;s P is equal to any times one plus R over m to the power of negative 70. So let&#x27;s use this equation to find our present value. So we&#x27;re given all of our variables on our right hand side are amounts is to know that our rate is 7% so much 70.7 over our number of compound in periods. In this case, we&#x27;re calm pounding semiannually, so that&#x27;s two times every year. So RM values, too. And then that&#x27;s times on the never years. So that&#x27;s eight years. That&#x27;s two times eight, which is 16. Okay, so now we&#x27;ll plug this into our calculator and we get a principle of 1153 and 41 cents

Amy Jiang · Answer

Okay, so we&#x27;re given that Ashley has 12 or 120,000. She decides to invest well, she decides to put some into a CD that earns 4% interest per year. So assume that X is equal to, um, the amount invested in the city. So we have that, um, that&#x27;s equal to X. And then we want to know the amounts invested in or low risk cock that 7% interest. So it&#x27;s put this as 4%. So out of our total 120,000 Well, we&#x27;re going to subtract that from the amount invested from our city, and that&#x27;s gonna be equal to for amounts invested at seven presents. Right? Because we&#x27;re only investing in two accounts and our amounts invested is a total of 120,000. So we want to know how much you earn If she invested each to earn interest of 7800. Okay, so let&#x27;s set these equal to each other. Let&#x27;s have 4% which is their 40.4 times X. We&#x27;re gonna add that to the amount invested in our several presents. So that&#x27;s 0.7 times 120000 and this is minus X and we have that the total amount earned. It just is $7.800. Okay, so let&#x27;s see, um, let&#x27;s multiply through that points where All seven times 120000 So he gets to a 0.4 x plus 8400 minus 0.7 That&#x27;s people to 78 It was Oh, so that&#x27;s isolates are constant. So I&#x27;m going to surcharge its halogen, or 8400 on both sides, and combine 84000.0 for minus 2.7 That&#x27;s a negative 0.3 X is equal to 78 year old girl when it&#x27;s 8400 So that&#x27;s equal to negative 600 analysis. All forex, when we have to do is divide by 0.3 The negative of that, and I get that X is equal to make 600 divided by points or negative points 03 and that&#x27;s equal to 20,000. So 20,000 is amount invested in our city, and then the amount invested in or seven percents. It&#x27;s 1200. Our star 120,000 minus 20,000 which is equal to 10 dozen is the amount invested. This is interceding and this is in our low risk stock.

Problem

Pick an appropriate solvent from Table 13.3 to di…

Problem 25 Hard Difficulty

Answer

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