To replace a gross income of $50,000 indefinitely at a 5% return, how much capital would be required?

To determine the amount of capital required to replace a gross income of $50,000 indefinitely at a return rate of 5%, a fundamental principle of finance can be applied that connects income generation with capital investment. This principle states that the annual income that can be generated from an investment is equal to the amount of capital multiplied by the rate of return.

In this scenario, the formula used is:

Annual Income = Capital x Rate of Return.

Rearranging this to find the required capital gives:

Capital = Annual Income / Rate of Return.

Substituting the values into the equation:

Capital = $50,000 / 0.05 (which is 5%).

Calculating this results in:

Capital = $50,000 / 0.05 = $1,000,000.

Thus, to generate a gross income of $50,000 indefinitely with a 5% return, it is necessary to have $1,000,000 in capital. This aligns with the explanation behind the chosen answer, as it accurately reflects the relationship between income and capital.