# Course 1, Week 2 Practice Quiz 1 Confusion

Hello community,

I am unable to deteremine how did I reach the solution to question 7. I just kept on doing trial and error with two equations and I got the answer 1666.66 which seemed close to 1600 so I selected it. The thing is I am still not able to understand what happened and how did I reach the solution. I do not understand the logic of the problem.

Kindly if someone can explain the problem. I will appreciate the help.

Thank You.

2 Likes

The questions in quiz get randomized. It will be really helpful if you share the screenshot of the problem. Ty

1 Like

Sure. Hereâ€™s the SS

2 Likes

Let us put x in CDs. Then we have, \begin{align} 2x + x + z &= 10000, \\ \frac{2}{100}2x + \frac{3}{100}x + \frac{4}{100}z &= 260 \\ \end{align} Now, solve for z. 17 Likes Thank Your for the reply. As I mentioned in my post that with trial and error, I was able to reach the solution just the way you wrote. But it was trial and error and I want to understand the logic behind this. Thank You. 1 Like Hold on! Does the 4% in Bonds not appear in your question? 3 Likes Yes, I was going to ask that question as well. It talks about three instruments, but I only see 2. Is the screenshot truncated somehow? 3 Likes I apologise for the confusion. Yes, the SS somehow truncated the bonds section, IDK why. I am having the 4% Bonds section. The thing that I do not understand is that why we first set the equation as 2x + x + z = 10000? 7 Likes Because that is the total cash involved, right? And they told us that the amount in savings is 2x the amount in CDs. This is â€śstory problemâ€ť time. Brings back memories of being in 8th grade. 8 Likes Was anyone able to understand the logic behind the solution? I am still trying to figure out how to set up the 3 equations. 1 Like Not to be pedantic, but technically there are three equations and the confusion for some may be better resolved by seeing the following three equations: I. s + c + z = 10000 (s, c, and z are amounts in savings, cds, and bonds respectively) II. 0.02s + 0.03c + 0.04z = 260, or 2s + 3c + 4z =26000 III. s-2c=0 (because s=2c, â€śhe put twice as much money in the savings account as in the CDsâ€ť) As @AeryB did above, you can substitute s=2c from III into I and II and reduce the system to two variables (s and z), or you can solve I, II, and III (without the substitution) using techniques taught. 9 Likes Hello, according to the text of the problem, you can set up the equations in the following way: s+c+z =10000 1.02s+1.03c+1.04z=10260 s=2c Solving this system yields to z=1600 If you put X into 2% interest account, after one year will have 1.02*X amount. That is the logic behind the equation nr. 2 Best regards 2 Likes This is mostly irrelevant for the purpose of this class, but in case someone finds this interestingâ€¦as an investment person, this how I think about a problem like this: The combination of assets has a 260/10,000 = 2.6% yield. The savings plus CD can be viewed as a composite security with weights 2/3, 1/3, so has a yield of (2/3)2% + (1/3)*3% =7/3 %. So we are just trying to find what weight w of the satisfies the weighted yield equation: 4w +(1-w)(7/3) = 2.6 â€”> w = .8/5 = .16 , ie 16% of the portfolio is in bonds, or 16%*10,000 =1600.

Of course, this ends up being equivalent to the more standard explanations given above.

2 Likes

@Inntr8

It was a really great way to think.
Thanks for sharingâ€¦

2 Likes

Guys, I still donâ€™t get it. Why is s = 2c? The problem says:

he put twice as much money in the savings account as in the CDs, and â€śzâ€ť money in bonds.

Doesnâ€™t it mean that s = 2(c + z)?

6 Likes

Pay attention to the comma in that sentence. Those are two separate clauses. So there are two statements there:

The money in savings (s) is twice the money in CDs (c).

z is the amount in bonds.

3 Likes

Thank you so much! English is not my first language, so that was a little confusing for me

4 Likes

I have the same issue, so maybe you could think of rephrasing the statement not to confuse non-native students? Thanks!

1 Like

Iâ€™ve also had trouble with this question. For me it feels the first part of week 2 is mostly the same as week one. But then this question requires you to make a big leap in reducing a description into a system of equations to solve. Iâ€™d prefer more instructions and questions around this concept.

3 Likes

I come back to it now a few hours later and still have trouble solve it.

2 Likes