Starting at age 30 (time period = 0), you have set a personal goal to retire at 60 and spend the first ten years of retirement living in Japan. To realize this, you plan to create a savings plan that involves making annual end-of-year deposits, with the amount specified as $C, starting at age 31. You will continue this disciplined saving practice until you are 60, ensuring you build up the necessary funds for retirement. Upon retirement, you aim to make a series of ten annual withdrawals, with the first withdrawal of $80,000 at age 60, to fund your lifestyle in Japan.
Calculate the total sum you'll need by age 60 to ensure you can withdraw $80,000 yearly for retirement living in Japan.