Step 1 :The gross income is the total income before any deductions or taxes. In this case, it would be the sum of the man's wages and the interest from his savings account. So, the gross income is \(32500 + 1500 = \boxed{34000}\).
Step 2 :The adjusted gross income is the gross income minus any adjustments. Here, the only adjustment is the contribution to the tax-deferred retirement plan. So, the adjusted gross income is \(34000 - 3800 = \boxed{30200}\).
Step 3 :The taxable income is the adjusted gross income minus the greater of the standard deduction or the itemized deductions. The itemized deductions are the sum of the interest on the home mortgage, the contribution to charity, and the state taxes paid. So, the itemized deductions are \(7500 + 2600 + 2000 = 12100\). Since the itemized deductions are greater than the standard deduction, we subtract the itemized deductions from the adjusted gross income to get the taxable income. So, the taxable income is \(30200 - 12100 = \boxed{18100}\).