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Question 283 ptsYou have been given SSO.000 to invest: you would Iike to invest part in a stock portfolio earning an average 10%,and the rest in an MMA earning on a...

Question

Question 283 ptsYou have been given SSO.000 to invest: you would Iike to invest part in a stock portfolio earning an average 10%,and the rest in an MMA earning on average 6%. How much should be invested in each to insure Bain of 9% of the total invested?537,000 in the stock portfolio and $13,000 in the MMA 537,500 in the stock portfolio and $12.500 in the MMA 537,000 in the MMA and $13,000 in the stock portfolio 537,500 in the MMA and $13.000 in the stock portfolio

Question 28 3 pts You have been given SSO.000 to invest: you would Iike to invest part in a stock portfolio earning an average 10%,and the rest in an MMA earning on average 6%. How much should be invested in each to insure Bain of 9% of the total invested? 537,000 in the stock portfolio and $13,000 in the MMA 537,500 in the stock portfolio and $12.500 in the MMA 537,000 in the MMA and $13,000 in the stock portfolio 537,500 in the MMA and $13.000 in the stock portfolio



Answers

An investor puts a total of $\$ 25,000$ into three very speculative stocks. She invests some of it in Crystalcomp and $\$ 2000$ more than one-half that amount in Flyboys. The remainder is invested in Zumcorp. Crystalcomp rises $16 \%$ in value, Flyboys rises $20 \%,$ and Zumcorp rises $18 \% .$ Her investment in the three stocks is now worth $\$ 29,440 .$ How much was originally invested in each stock?

So we'll consider an investment strategy. Um and so we have $300,000 to invest. And so we're gonna invested in three different stocks. General Motors Pepsi. And ceremony General Motors yields um 2.7% Pep Ceo is 1.7% interest. Um and dividend and Sara Lee is 2.4% is a dividend. I'm assuming those are per year. Um Obviously those are roughly what you might expect some companies like that. Um So we see here they've also given this constraint here that the amount vested in Pepsi needs to satisfy this equation. So we need to satisfy this for whatever reason because otherwise we don't have a have a well defined problem. So we need this extra constraint. So we have two constraints. Then We have the constraints are total money to invest, has to be 300,000. And while they're given this kind of artificial constraint that says we've got to put some at least some money and pepsi for whatever reason. Um Otherwise I think we just get rid of this because its dividend is pretty low. So what we want to do is we want to maximize our yield amount of money. We're getting back as a dividend kind of like our interests. Um We expect um govern these two constraints. So we have two constraints. Now. So this is a function of G. P. Or this is a function of gps Lander, one or two. So we have we have five partials to do. So the partial respected G. Set that equal to zero expected piece that that equals zero expect us that equals zero. Then the partial with respect to the Lagrange multipliers. We just get these two constraints back. Um And now it's a matter of just eliminating variables we could eliminate landed to in terms of land a one here put that in here eliminate landed one in terms of P. And put it back in and back substitute. And in the end what will kind of wind up getting is the amount that we should invest in general motive Is about $157,792. $8,500. And then summarily $1,100,132,708. Um So you can see that makes some sense because proxy has the lowest um yield here. But again because of this constraint we need to have at least sometimes in our portfolio. And so what we're going to yield is about $7,614 per year. And that's about 2.5% yield on our $300,000. And that again makes sense because it's somewhere in between here right? Um And this is dragging it down the somewhere between here. So it makes it makes some sense but where we're at. Yeah

Were given that $24,000 is invested at 3.5% and 5%. Simple interest. There was $930 earned an interest. We need to find out how much of the original amount the $24,000 was invested at 3.5%. So we have um What we invested in 3.5% plus what we invested in the other percent is equal to the 24,000. And then we have our interest equation which is we've got to change our percentage to decimals. So we have 035 X. Plus 350.5 Y. Is equal to 930. So now we saw. So the first thing we're gonna do is multiply by 1000 to get whole numbers. So we get X plus Y. Is equal to 24,000. When we get 35 x plus five y. is equal to 93 groups 93 123 Zeros. So now we're going to multiply. Yeah.

$24,000 and is invested at 3.5 and 5% simple interest, $930 of interest was earned. We need to find out how much was invested at 3.5%. So we have our 3.5% amount Plus our 5% amount. And that was a total of $24,000. And then we have to change our percentages into decimals. So .035 times x plus .050 Times Y. is equal to the $930 in interest. So we're first gonna multiply our decimal equation by 1000 to get whole numbers. So we get X plus Y is equal to 24,000 And we get 35 x plus 50 y. 50 Y. Is equal tune 930,000. So now we're going to multiply our top equation by negative 50. So we can cancel out the wise because we want to find out the 3.5%. So this is negative 50 X minus 50 Y. Is equal to 24,000. Oops 24,000 times negative 50 Comes out to be negative 120 no 1.11.2 million. And then our bottom equation stays the same, which is 35 x plus 50 y. Is equal to 930,000. So our wise cancel out 50 -35, leaves us with -15. And then The 1.2 million And the 930,000 are subtracted. That gives us -270000. And we divide both. We divide by negative 15 And we get X. is equal to 18 1000. So that tells us that $18,000 was invested at 3.5%.

So we didn't some financial planning or we have $6000 to invest, 6% savings account and 12% for the mini mall. So we have 6%. Not since savings, 12%. And that's in a mini mall. Um, and then the earned $540 in the first year. 5 40 The silence has earned. So just say, X is our savings account. Why is our mini mall I know that altogether x plus y makes the $6000 6% earned from saving. So move the decimal twice, 12% from a minimal move, the decimal twice, $540 earned. I'm gonna multiply the top equation because I want to eliminate. They're gonna go 0.6 because then the exit will match up. So bringing that equation down here, if 0.6 x plus 0.6 why equals $360 then I'm able to subtract those equations from each other. 0.0 point 6.12 y minus 0.65 and then 5 40 My industry sixties 1 80 Oh, good. Yeah. Divide by 0.6 and you'll have your wife value. So what does that tell me? Why is equal to three 1000 once I know Why is 3000? I know that X has to be well, you have $6000 total. So acts also in the studio 3000 then there you go.


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