[Math] How to solve this stock market word problem

algebra-precalculussystems of equations

I have the following problem:

Mr. Fortuna has $\$100,000$ dollars to invest in stocks, bonds and an account in the money market. Shares have a recovery value of 12% per year, while bonds give 8% a year and the money market account, 4% per annum. They have agreed that the amount invested in the money market must be equal to the sum of 20% of the amount invested in shares and 101010%10% of the investment in bonds. How should you distribute your resources if you need an annual income of $10,000$ for your investments?

More than the solution itself, I want to know how to solve this problem step by step.

How can I get the correct equations connecting the given information?

Best Answer

Rewriting the original problem:

Mr. Fortuna has $100000$ dollars to invest in stocks, bonds and an account in the money market.

  • Shares gives him a return of $12\%$ per year.
  • Bonds gives him a return of $8\%$ per year.
  • Money Market give him a return of $4\%$ per year.

And he decided to allocate his resources in the next way:

"He decided that the amount invested in the money market must be equal to the sum of $20\%$ of the amount invested in shares and $10\%$ of the investment in bonds".

Finally the profit must be $10000$.

You need three variables:

$s$: amount invested in shares

$b$: amount invested in bonds

$m$: amount invested in money market

The allocation constraint is:

$$m=20\%s + 30\% b$$

The profit of each asset is equal to the return multiplied by the amount invested:

$$12\% s + 8\% b + 4 \% m= 10000$$

And finally all the money invested must sum $100000$:

$$s + b + m= 100000$$

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