Problem

Investment problems. A financial planner invested…

08:47

Problem 27 Medium Difficulty

Investment problems.
A newly hired MBA graduate received an 18,000 dollar signing bonus from her employer. She invested part of it in a credit union account earning 3% annual simple interest and the rest in utility stocks that suffered a 7% loss of value. The net income from both investments for the first year was only 90 dollar. How much of her bonus was originally placed in each investment?

Answer

Credit union: $\$ 13,500 ;$ stocks: $\$ 4,500$

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Chapter 2

Equations, Inequalities, and Problem Solving

Section 6

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Video Transcript

memory. It's a newly hard and be a graduate received $18,000 signing bonus from her employer. She invested part of it in a credit union account, earning 3% annual simple interests and the rest and utility stocks that suffered a 7% loss of value. The net income from both investments for the first year was only $90. How much of her bonus was originally placed in each investment? So I started off by making a chart that has the equation p times our terms. T is equal to ay one row represents the credit account. The other road represents the stocks. So we're gonna fill out this chart to help us all for how much she put into each account. The total that she earned in the first year is $90 so that's a total interest earned, and that's over the course of one year. So I'm gonna put one in the tea column for both types of accounts and then for the credit account, I'm gonna say that the principal value or the original amount put in that account is represented by X, and the rate for the credit account is 3% so as a decimal, that 0.3 and then for the stocks, the principal value and the socks is gonna be 18,000 minus the X. Because the total month, as she put into both accounts, was 18,000 and the interest on the socks was, she lost the 7% value. So instead of positive, it's gonna be negative 0.7 So now, to write out the equation for the interest for each type of account or each step of investment for credit, it's gonna be 0.3 x Because we're multiplying all these together. The P times are times t so that 0.3 x for stocks, it's gonna be negative 0.7 times 18,000 minus X. Now we're gonna write out an equation. We're gonna combine the interests equations and make it equal to the $90. So we have 0.3 x minus 0.7 times 18,000 minus X is equal to 90. Then, from here, we're gonna multiply both sides of the equation by 100 because we want to get rid of the decimals. So then we have 100 times 0.3 x and that is three X. Then we have 100 times negative 0.7 which is just gonna be negative. Seven. And we still have to multiply that by 18,000 minus X is equal to 9000. Then, from here, we're gonna have to distribute the negative seven to the 18,000 CZ well, asses to the negative X. So we have three X negative seven times 18,000 is gonna be negative 126,000 and the negative seven times negative X is gonna be positive. Seven x is equal to 9000. And then from here, we're gonna combine like terms. We're gonna combine the three X and the seven X so three X plus seven X is 10 x so we have 10 X minus 126,000 is equal to 9000. So now we have a two step equation. So the first thing that we're gonna have to do is move the constant to the other side. So to get 126,000 to the other side of the equation, we're gonna add 100 26,000 to both sides so that with the way that I have it written, it's the, um, numbers are not lined up, but we have 126,000 negative, 126,000 plus 126,000 which become zero and then we're left with 10 X is equal to 9000 plus 126,000 and that equals 135,000. Then we want to isolate the X. We want to get the ex alone, so we're gonna have to divide 10 on each side of the equation. 10 divided by 10 is one. So then we're left with X is equal to we have 135,000 divided by Ted. And that is 13,500. So we know that $13,500 was invested in the credit account and to figure out how much was invested in the stocks. All we have to do subtract 18,000 minus the 13,500 and that's gonna be 4000 500. So we know that $4500 was invested in socks, and that is our solution to our problem.

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