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.

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.

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.

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

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.

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.