You plan to retire $40$ years from now. You expect that you will live $30$ years after retiring.

You want to have enough money upon reaching retirement age to withdraw $$150,000$ from

the account at the beginning of each year you expect to live, and yet still have $$2,00,000$ left

in the account at the time of your expected death $(70$ years from now$).$ You plan to

accumulate the retirement fund by making equal annual deposits at the end of each year for

the next $40$ years. You expect that you will be able to earn $10\%$ per year on your deposits.

However, you only expect to earn $7\%$ per year on your investment after you retire since you

will choose to place the money in less risky investments. What equal annual deposits must

you make each year to reach your retirement goal?