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Hmcints Aum'Aan| IC QQFE Q10 0Subraty $ $ /oqus UeecNotesaecount xecutiva deposited #Jo QOQ Into two simple (nteteet accounts On the Eaxefreo account the annua...

Question

Hmcints Aum'Aan| IC QQFE Q10 0Subraty $ $ /oqus UeecNotesaecount xecutiva deposited #Jo QOQ Into two simple (nteteet accounts On the Eaxefreo account the annua simple interost mate and on the money market fund the annual simpla Interust rate 5844 Hioi mmch should be Invested each aocount that both accounts Aa Ine *MU Hmml iutenest tat tuea #CCUMGmoney maAetpuuts Frevlous Ansna AuModktath| 9 24005cubnisEiona U-Hniing

Hmcints Aum'Aan| IC QQFE Q10 0Subraty $ $ /oqus Ueec Notes aecount xecutiva deposited #Jo QOQ Into two simple (nteteet accounts On the Eaxefreo account the annua simple interost mate and on the money market fund the annual simpla Interust rate 5844 Hioi mmch should be Invested each aocount that both accounts Aa Ine *MU Hmml iutenest tat tuea #CCUMG money maAet puuts Frevlous Ansna AuModktath| 9 24005 cubnisEiona U- Hniing



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You are given the yearly interest earned from a total of $18,000$ invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate. $$\begin{array}{lll} \text {Yearly Interest} & \text {Rate 1} & \text {Rate 2} \\ \$ 1182 & 5.6 \% & 6.8 \% \end{array}$$

Here in this question. Let eggs be the amount. Ambassador 175% Hawaii Be the amount invested art for what? 25 person no set of the kitchen. Total investment Huge. $18,000 and totally interest. What you gonna do? 6. $84. Number two We Christians are explosive. Y Did you go to eight Intelligent. And this is total investment. The question one total investment and zero point 20275 x Yes. Do you want Do you have 4 to 5? Why? MM. Each 6. $84. This is a Kindle Kison 2.75% means just remove that a small point and want to play indoor Then So zero point this comes the door. Zero point You don't know 75 That's all for y. We can sell for away using a cousin one explodes where you hear it It's intelligent or why is equal to it's intelligent minus six. Now this after suit this value of why any question took So here the personage zero point 0275 x plus Gerald won't do you know for five y means here 18,000 miners x 6 80 Poor dollar. No, it's all this. Zero point 0275 x plus. Multiply these two. This is 7 65. Uh huh. Minus 0.4 to 5 weeks. It's called oh, six AP poor. Or this is the difference between the two. Europe weren't 015 X is equal to 6. 84. Your difference between 7. 67 6. 84 u T. One mhm now X physical too. How intelligent. 400. This is 81 David away. You're open. You know what? Okay, We got this among 5400. No so far away. Using your question One. Yeah. One here actually got 5400 explosive series age intelligent. So why is your to it? Intelligent? Minus 5400. You teach You're intelligent. 600. So we got the value. Excess X is equal to five Children. Food hunter. And why is he called? Oh, 20,000 600 dollars. No pigeon? No. This is the answer.

Here we will use were able to represent or non data Solarte eggs the mountain, Mr It 6% And why the amount invested it 3% total investment amount $18,000. So here explains why you were too intelligent. This is the first case when I got now the interest for the two investment commanded. 8 40 Total interest is here pro talented. 8. $40 and interest for the two investment company Day for $2. So both third six personal. 3%. So 6%. 6% investment It's X amount and 3% investment. Amount it Why and right up until the expression door zero point 06% And here 0.3% or interested, 0.6 x and zero point 03 Why pay using this table? Usually we can get take a listen to so here, totally interested it for $2 or Europe want euro six plus 0.3 y is equal to 8. $40. This is a question, too. Dickerson won it explosive. Why did you go to it? Too intelligent. So the two questions we got X plus y musical to you too intelligent and 0.6 x Class 010 three way. Izzy Gould Oh, 8. 40. This can be solved as a tradition, method or addition. Method, soft edges and material work well here because both terrible Cinda first question alcohol patient of one extend way so well, as soon as 11 Also a recent works well here. If we multiply the first question by minus European Jurassic Sarge, European geometry. So our recent adding the secret essentially eliminate the variables. Both self teaches another recent method. We can solve the problem next to today. Artisan method. Our decent little X plus y Yes, you do it intelligent Will multi place multiply by my nurse. You're a point, Juro. Six. So here explores where you are minus 0.6 eggs and minus minus. European viruses also multiple right away. So my next 0.6 way Judo Six. Why is he called? Oh, 100 and second location, right. 0.0 point 06 Eggs. Applause 0.3 y Is he dildo 8 40 Here. No changes, no change. So here Europe weren't due to six x applause. Europe €1.3 way is he gonna do yet? 40 are the two equations So 0.6 plus minus cancer here minus 0.65 and here 0.3 ways. So minus 0.3 y. Did you call Joe? Who? 40 again? What is the value of y? What is he going to? This is minus minus 2. 40. Never heard away my next 0.0 three. Uh, this is what is your do? Yeah, I told you. Now you go to the value of why, By putting this value for any question one we can get the value of thanks. So question one is X plus y. Is he going to do eight Intelligent for the value of our here. Explosive. Intelligent? Is your dough h intelligent or exceptional? Do 10,018 minus eight the intelligent. So now you've got both the value of exertion. Why buy this edition method so excess to intelligent alert? I don't know what it is you told you dollar. This is a mountain dollar. So this is the answer

All right. So this is a pretty interesting application of systems of equations where we have two different accounts and we have some relationship between the accounts of their same amount of time. So in this case, we've got I'm calling it an account and account be and account A. You're witnessing a 6% annual interest rate. That's 6% growth every year and account B. You have 9% growth every year. And we are told that the accounts have the same amount of money after one year. So the accounts are equal after one year, and we have to figure out right how much is deposited in each account. Um, this is a classic example of systems of equations because we have multiple pieces of information which we can create equations for hence multiple equations. First piece of information. We know. All right. Is that account A. Let's say we deposit a dollars. All right, let's match it up into account A and we deposit the dollars into account. We are told in the problem that there are $6000 that's been deposited, so it must be is 6000. It is split into training and competing. We also know that account a after one year has grown 6%. Well, how do we represent 6% growth? 1.6 Sunday? Right? That is the amount of money in account A after one year. And that has to equal the amount of money in account. See, after one year, right. The accounts are equal after one year. Well, the amount of money in account B after one year, 9% growth is to simply 1.9 times B. And this is a system of equations, right? Two equations, two variables. Bing, bang, boom. Let us solve. Um, always there are multiple ways to solve. In this case, I'm simply going to solve the second equation for a and then plug it into the first equation to solve. So how do we solve for a divide by 1.6 from both sides that will get this eight equals 1.9 divided by 1.6 Gives us 1.283 Um, had more decimal point to remember. If you're using a calculator, preserve those decimals until the end of the question. I am going to write it with 566 just for shorthand here. But this is something that we can plug into equation aid. So that's what I'm gonna do. I'm gonna substitute a 41.283 b into equation A. No, that's still plus B is equal to six Elton. So this is just right, um Equation equation one for lack of confusion. Right, This equation one. This is something with one variable one equation. We can solve it. Combine like terms. Divide by 2.283 That's what you get when you add the That gives us be equal to 2958.14 So that's the amount of money that was deposited into account. Now, if we also need to find the amount of money deposited into account A well, you can simply subtract 6000 minus that right, because they have to add up to be 6000. So essentially, we're just looking back into the equation A. And that gives us our answer for the amount of money in equation. A foreign account, which is 3000 and 41 point six

So for this question, you're asked, You have to savings account and each with an initial principal of $1000. The no meal rate for both accounts is 5.25% per annum. In the first account, interest is compounded semi annually. In the second account, interest is compounded continuously. How much more is in the second account after 12 years? So for the first account, we're going to use the formula of a Oh, let me just write that it is the first account first account. So we use the formula A is equal to p one plus r to the power of and and this goes as follows Suite of A is equal to 1000 one plus and it is zero point 05 25 divided by two because it's compound id, semi annually and then 12 years. But you have two times by two because once again, their semi annually, so he's gonna be 24 compounding periods. Now we have 1000 one plus 1.0 26 25 and to the power of 24. So when you do that, you're gonna be left with your amount after 12 years is going to be one 1008 162 0.413 now for the second account, the second account. It's continues, calm pounding, so we're gonna have to use a different formula. And that formula is a is equal to p times Mueller's number to the power of our teeth. So in this case, a is going to equal to 1000 as their principal times he to the power of 0.525 times 12. So now we have 1000 is equal to e to the power of 0.63 So when we do this, we get 1000 times 1.878 and that is in the total amount after 12 years, and the account is going to be equal to $1877.611 So, um, now we need to calculate the difference between the two accounts, and the difference between the two accounts is you've dis attract the to, and when you subtract them, you get 15.198 or you can just dio 15.2. So, uh, we can say that the second account is greater than the first account by $15.2 and that is our final answer.


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