You wish to retire in 12yrs and currently have $50,000 in a savings account yielding 5% annually and $100,000 in quality “blue chip” stocks yielding 10%. If you expect to add $30,000 at the end of each year to your stock portfolios, how much will you have in your retirement fund when you retire? What rate of return must you earn on your retirement funds if you want to withdraw $102,000 per year for the next 15yrs after retirement?

To calculate the future value of your retirement fund, you need to calculate the compounded growth of your savings and stock portfolios.

1. Retirement fund after 12 years:
Firstly, let's calculate the future value of the savings account and stock portfolios separately. In order to do that, you can use the compound interest formula:

Future Value (FV) = Present Value (PV) * (1 + interest rate)^number of periods

For the savings account:
FV_savings = $50,000 * (1 + 5%)^12

For the stock portfolios:
FV_stocks = $100,000 * (1 + 10%)^12

Next, calculate the future value of the annual additions to your stock portfolios over the 12-year period:
FV_annual_additions = $30,000 * [((1 + 10%)^12 - 1 ) / 10%]

Finally, calculate the total retirement fund by adding up the future values:
Total retirement fund = FV_savings + FV_stocks + FV_annual_additions

2. Rate of return needed for withdrawals after retirement:
Given that you want to withdraw $102,000 per year for the next 15 years, you need to calculate the rate of return required to sustain these withdrawals.

This can be found using the present value of an annuity formula:

Present Value (PV_annuity) = Annual Withdrawal * [1 - (1 + interest rate)^(-number of periods)] / interest rate

Rearrange the formula to solve for the interest rate:

interest rate = (Annual Withdrawal / PV_annuity)^(1 / -number of periods) - 1

Substitute the values:
interest rate = ($102,000 / PV_annuity)^(1 / -15) - 1

Note: In this explanation, we assume that all calculations are done on an annual basis.