Given tax brackets of 10 per cent on first 22000, 12 per cent on the next 68000, and 22 per cent on the next 10000, find optimal balance of withdrawal rates from taxable and tax free accounts to arrive at 100000 annual income with minimal tax. The total balance is 1000000, with 700000 taxable and 300000 tax free, so that the account is depleted in 30 years.
To find the optimal balance of withdrawal rates from taxable and tax-free accounts in order to achieve an annual income of $100,000 with minimal tax, we can set up a calculation based on the given tax brackets and account balances.
Let's assume a withdrawal rate "x" from the taxable account and a withdrawal rate "y" from the tax-free account. The total annual income can be calculated as follows:
Total Income = (Taxable Account Balance * x) + (Tax-Free Account Balance * y)
We want to find the values of x and y that maximize the total income while minimizing the tax paid. To do this, we need to consider the tax brackets and calculate the tax on each portion of the income.
First, we need to determine the taxable income. We can start by subtracting the tax-free portion from the desired annual income:
Taxable Income = Total Income - Tax-Free Account Balance
Next, we calculate the tax paid on each portion of the taxable income based on the given tax brackets:
Tax1 = 0.10 * 22000 (10% tax on the first 22000)
Tax2 = 0.12 * (Taxable Income - 22000) (12% tax on the remaining amount up to 90000)
Tax3 = 0.22 * (Taxable Income - 90000) (22% tax on any amount above 90000)
Now we can calculate the after-tax income:
After-Tax Income = Total Income - (Tax1 + Tax2 + Tax3)
Finally, we can set up an equation to find the values of x and y that maximize the after-tax income:
After-Tax Income = (Taxable Account Balance * x) + (Tax-Free Account Balance * y)
Additionally, we need to ensure that the account balances are depleted in 30 years. We can set up an equation based on the account balances and the withdrawal rates:
30 * (Taxable Account Balance * x + Tax-Free Account Balance * y) = 700000 + 300000
Now we have a system of equations that we can solve to find the optimal values of x and y that satisfy all the given conditions. This can be done using numerical methods or software such as Excel or MATLAB.
Please note that this is a simplified approach and does not take into account factors such as inflation, investment returns, or changes in tax laws. It's always best to consult with a financial advisor or tax professional for personalized advice in your specific situation.