Final answer:
To earn $225 a month from an investment that yields a 7 1/2% annual return, you would have to invest $36,000. This is calculated by first determining the total annual income required ($225 * 12 = $2700), then dividing that annual income by the annual return rate (0.075) to find the principal investment.
Step-by-step explanation:
To determine the amount one must invest to earn $225 a month from an investment yielding a 7 1/2% annual return, we can set up an equation based on the annual income desired from the investment. Since the question asks for a monthly income, we first find the annual income by multiplying $225 by 12 months, giving us $2700 annually.
We let P represent the principal amount to be invested. The annual return on investment (ROI) at 7.5% can be represented as P times 0.075. Setting up the equation, we have:
P * 0.075 = $2700
Dividing both sides of the equation by 0.075 to isolate P, we get:
P = $2700 / 0.075
Calculating this gives:
P = $36,000
Therefore, to receive $225 a month from an investment with 7 1/2% annual return, you would have to invest $36,000.