Charles Juniper, 24, is about to begin his career as a rocket scientist for the European Space Agency. Being a rocket scientist, Charles knows that he should begin saving for retirement immediately. Part of his inspiration came from reading an article on retirement savings plans in The Economist, where he saw that the ratio of workers paying taxes to retirees collecting checks is expected to drop dramatically in the future. In fact, the ratio was 8.2 workers for every retiree in 1960; it is 3.4 today and is expected to drop to 2 workers for every retiree by 2050. Charles’s retirement plan pays 10 percent interest annually and allows him to make equal yearly contributions.

Upon retirement, Charles plans to buy a new boat, which he estimates will cost him \($320,000\) in 41 years (he plans to retire at age 65). He also estimates that in order to live comfortably, he will require a yearly income of \($85,000\) for each year after he retires. Based on family history, Charles expects to live until age 80 (that is, he would like to receive 15 payments of \($85,000\) at the end of each year). When he retires, Charles will purchase his boat in one lump sum and place the remaining balance of his savings into an account, which pays 5 percent interest, from which he will withdraw his \($85,000\) per year. If Charles’s first contribution is made 1 year from today and his last is made the day he retires, how much money must he contribute each year to his retirement fund?