1. For an employee hired at age 35 at a salary of 50 000, it is estimated that an amount of 500 000 is needed at at the normal retirement age of 65 to buy an appropriate pension. For exit from the plan before age 65 the accumulated amount of contributions with interest is returned to the employee. Find a formula to calculate the contribution rate c, assumed to be made at the beginning of each year.
2. Suppose that in the situation described above, the contributions are split, with the employee paying 40% and the employer the remaining 60%. For participants exiting the plan after 5 years, the total of all contributions with interest is returned at the end of the year of leaving. For those exiting in the first 5 years only the employee's own contributions with interest are returned. Find an equation to determine the contribution rate c.