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.
The questions in quiz get randomized. It will be really helpful if you share the screenshot of the problem. Ty
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.
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.
Hold on!
Does the 4% in Bonds not appear in your question?
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?
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?
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 “story problem” time. Brings back memories of being in 8th grade. 
Was anyone able to understand the logic behind the solution? I am still trying to figure out how to set up the 3 equations.
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, “he put twice as much money in the savings account as in the CDs”)
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.
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
This is mostly irrelevant for the purpose of this class, but in case someone finds this interesting…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 —> 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.
It was a really great way to think.
Thanks for sharing…
Guys, I still don’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 “z” money in bonds.
Doesn’t it mean that s = 2(c + z)?
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.
Thank you so much! English is not my first language, so that was a little confusing for me
I have the same issue, so maybe you could think of rephrasing the statement not to confuse non-native students? Thanks!
I’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. I’d prefer more instructions and questions around this concept.
I come back to it now a few hours later and still have trouble solve it.
