Answer Happy

A Plus Insurance Corp. offers a lifetime annuity to retiring accountants. For a payment of $x at age of 65, the company offers to pay the retiring accountant an amount of $600 per month until death. Suppose Mr. Smith, who just turned 60, is considering this offer. If the remaining life expectancy of Mr. Smith is 30 years from retiring, i.e., from turning 65, and the effective annual rate on this annuity is 6.78%, find x, i.e., find how much Mr. Smith needs to pay today at age 60 to guarantee $600 a month from the age of 65 until death. (Keep your answers to 5 decimal places, i.e., write 0.567% as 0.00567 and not 0.006).