What interest rate would need to be set on a for-profit bond to match the after-tax income of a not-for-profit bond paying 5 percent interest for John Richards, who is taxed at 30 percent?

To determine the interest rate that a for-profit bond would need to offer in order to match the after-tax income of a not-for-profit bond that pays a 5 percent interest rate, one must consider how taxes affect income from these investments.

The not-for-profit bond is tax-exempt, meaning that John Richards will receive the full 5 percent interest without any deductions. Therefore, the after-tax income from this bond is simply 5 percent.

Now, for the for-profit bond, the interest earned will be subject to taxation. To find the interest rate required on this bond that would give the same after-tax income as the not-for-profit bond, we need to set up the equation based on after-tax income.

If the interest rate on the for-profit bond is denoted as "r," the after-tax income from the for-profit bond would be calculated as follows:

After-tax income = r × (1 - tax rate)

In this case, the tax rate is 30 percent, or 0.30. Therefore, the formula becomes:

After-tax income = r × (1 - 0.30)

After-tax income = r × 0.70

To match the after-tax income of the not-for-profit bond,