Final answer:
To find the principal investment that earns a monthly income of $675 at an annual interest rate of 7 1/2 percent, we calculate the annual income and then rearrange the simple interest formula. The calculation reveals that the required principal investment is $108,000.
Step-by-step explanation:
The question is asking to determine the principal investment amount that, at an annual interest rate of 7 1/2 percent, would yield a monthly income of $675. To find the principal, we can use the formula for simple interest, which is Interest = Principal × Rate × Time. Since we are given a monthly income, we should first find the annual income which would be $675 × 12 months = $8,100. Now, assuming that the entire annual income is generated from interest, we can rearrange the formula to solve for Principal: Principal = Interest / (Rate × Time).
Given:
Annual Income (Interest) = $8,100
Annual Interest Rate (Rate) = 7.5% or 0.075
Time = 1 year (since the rate is per annum)
So, the principal investment is:
Principal = $8,100 / (0.075 × 1)
Principal = $8,100 / 0.075
Principal = $108,000
Therefore, a monthly income of $675 represents an annual return of 7 1/2 percent on an investment of $108,000.