You have just turned 30 years old and have accepted a new promising position in one of the big banks from your 30 years old birthday. Now you want to decide how much money to put into a retirement plan. The plan works as follows:

Every dollar in the plan earns 6.5% p.a. You cannot make withdrawals until you retire on your 65th birthday. After that you can withdraw the money to fund your day to day expenses. Your life expectancy is 93 and you will work until you turn 65. You want to live a comfortable during retirement so you estimate that you will need $100,000 per year, starting at the end of the first year of retirement, and ending on your 93th birthday. You will contribute the same amount to the plan at the end of every year that you work.

How much do you need to contribute each year to fund your retirement ? please show your working steps, formulas, and calculation in details.