Problem

Investment problems. Equal amounts are invested i…

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Problem 24 Medium Difficulty

Investment problems.
A financial planner recommends a plan for a client who has $\$ 65,000$ to invest. (See the chart at the right.) At the end of the presentation, the client asks, "How much will be invested at each rate?" Answer this question using the given information.

Answer

42200 in mini malls and 22800 in bonds

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Precalculus

Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 6

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Video Transcript

problems. 24 reads. A financial planner recommends a plan for a client who has $65,000 to invest. See the chart at the right. At the end of the presentation, the client asks how much will be invested at each rate and said this question using the given information. So this is our chart right here. I made our own chart with the equation. P temps are tens. T is equal to ay and separated into two rows, with mall being one of the categories and bonds being the other category. So we're gonna first start off with filling out that the total interest earned in the first year is going to be $6477.60. So we're gonna put that in our chart, and then our time is gonna be one year. So we're just gonna put one in both rose and then for our rate for the mini mall. It's a 12% annual rate. So that means as a decimal, it's gonna be zero points. Well, and then for bonds, the rate is 6.2%. So as a decimal, that's gonna be 0.62 So the amount that's going to be invested in the mall, I'm gonna use X two to note that amount and then for bonds since the total $65,000 our value that's gonna be put into bonds right now is gonna be 65,000 minus X and then to find our entries interest, we're gonna have to most by the principal times rate times time. So from all, it's gonna be 0.12 x for bonds. It's gonna be zero point 062 times 65,000 minus X. So we're gonna write an equation that includes the two interest quantities equaling totaling the 6477.60. So we have 0.12 x plus 0.0 62 time 65,000 minus X is equal to 6477 0.60. So we want to get rid of these decimals right here. So we're gonna multiply both sides of the equation. By 1000 we have 1000 times 0.12 X, which is going to be 120 x plus 1000 times is 0.0 62 which is gonna be 62 and then we still have to multiply the 62 by the 65,000 minus X and then 6477.60 times. 1000 is 6,477,000 and 600. Then, from here, we're gonna have to distribute the 62 to the 65,000 as well as the negative X. So we have 100 and 20 X plus 62 times 65,000 is four million and 30,000. Then we have 62 times negative X, which equals negative. 62 X is equal to the 6,477,600. And then from here, we're gonna combine like terms. So we have 120 X minus 62 X, which is 58 x plus. The 4,030,000 is equal to this. 6,477,600. So this is a two step equation. So we want to get the 4,030,000 to the other side. So we're gonna subtract that value on both sides. So 4,030,000 minus itself is gonna be zero. So then we're left with 58 x is equal to And then when we subtract 6,477,600 minus the 4,030,000 it's gonna leave us with 2,447,600. Then, from here, we wanna isolate the variables. So we're gonna divide 58 on each side. 58 divided by 58 is one. So we're left with X is equal to, and 2,447,600. Divided by 58 is gonna be 42,200. So that means that $42,200 was invested in the mall. And to figure out how much was invested in the bonds, we have to subtract the 65,000 minus the 42,200. So we have 65,000 minus 42,200 is equal to 22,000 $800. So $22,000.22,800 dollars was invested in the bonds, and that is our solution to this problem.

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