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:
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 $100000$:
$$s + b + m= 100000$$