Problem

Uniform motion problems. During a storm, two team…

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Problem 28 Medium Difficulty

Investment problems.
A financial planner invested a portion of his client's 190,000 dollar in a high-yield mutual fund that earned 11% dollar annual simple interest. The remainder of the money was invested in a mini-mall development. Unfortunately, that investment lost 25% of its value the first year. Find the amount originally made in each investment if the first-year net income was 6,500 dollar.

Answer

16500 and 10000

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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

problem, 28 reads. A financial planner invested a portion of his clients $190,000 in a high yield mutual fund that earned 11% dollar annual simple interest. The remainder of the money was invested in a mini mall development. Unfortunately, that investment lost 25% of its value the first year. Find the amount richly made in each investment if the first year net income was $6500. So I started by making a chart that includes the equation P times are times to use Equal toe I and one of the Rose will be the information for the mutual funds, and then the other road will be for the mall development. So we're gonna start by writing that the total amount earned from the investment was $6500 and this is after one years to the time for both investments is gonna be one. And then I'm gonna say that X is going to represent the amount that was invested in the mutual fund and the mutual fund had an 11% interest rates. So as a decimal, that's gonna be 0.11. Um, since we don't know what value was invested into the mall or the mutual fund, but we know that a total of $190,000 was invested into both. The value that I'm gonna put represent The principal put into the mall is 100 and $90,000 minus X. And because the mall lost its value instead of a positive decimal, we're gonna have a negative decimal, and it lost 25% of its value. So as a decimal, 25% is 0.25. Then from here to find the interest, we're gonna have to multiply. The P times are times T. So for the mutual fund, interest is your 0.11 X and then for the mall. It's gonna be negative. 0.25 times. Ah, 190,000 minus X. And then from here, we're gonna form an equation based on the information in the eye column. So we have 0.11 x minus 0.25 times 190,000 minus x is equal to 6500. And then before we can even start to solve this equation, we're actually gonna most by both sides of the equation by 100 to turn the decimals into whole numbers. So we have 100 times 0.11 x, which gives us 11 X and then we have 100 times negative 0.25 which gives us negative 25 and we still have to multiply that by the 190,000 minus X is equal to we have 650,000. So from here, we're going to distribute the 25 the negative 25 to the 190,000 as well a cz to the negative X. So we have 11 x negative 25 times positive. 190,000 is gonna be negative. 4,750,000 and then we have negative 25 times negative X, which will be positive. 25 x is equal to 650,000. And then we're gonna combine our light terms. So we're gonna do 11 x plus 25 x, and that equals 36 x minus four million 750,000 is equal to the 650,000. And then from here, we're gonna add 4,750,000 to both sides of the equation and so on the right side of the equation, I'm not able to line up the decimal points. If we have negative 4,750,000 plus 4,750,000 that would equal zero so we can cross it out and we're just left with 36 X and then we have 650,000 plus 4,750,000 and that's gonna be equal to 5,400,000. And then from there we're gonna divide both sides by 36 because we want to isolate the ex who want to get the ex alone. We have 36 divided by 36 which is gonna be one. So then we're left with X is equal to we have 5,400,000 divided by 36 that's 150,000. So that means that $150,000 was invested in the mutual fund. And then to find out how much was vested in the mini mall development, we're gonna have to subtract 190,000 minus the 150,000 which is 40,000. So that means that for $40,000 was invested in the mall. So that is our solution to this problem.

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