NO.PZ2020011901000037
问题如下：
Suppose that in a certain defined benefit plan the following simple situation exists. Employees work for 40 years with a salary that increases exactly in line with inflation. The pension is 60% of the final salary and increases exactly in line with inflation. Employees always live for 25 years after retirement. The funds in the pension plan are invested in bonds that earn the inflation rate. Which of the following is the best estimate of the percentage of the employee’s salary that must be contributed to the pension plan? (Hint: You should do all calculations in real rather than nominal terms so that salaries and pensions are constant and the interest earned is zero.)
选项：
A.37.5%
43.75%
22.5%
27.5%
解释：
A. The employee’s salary is constant in real (inflation-adjusted) terms. Suppose it is X. The pension is 0.6X. The real return earned is zero. The pension plan contributions therefore grow to 40XR where R is the (employer + employee) contribution rate as a percentage of the employee’s salary. The present value of the benefits is 25 * 0.6X = 15X. We therefore require 40XR = 15X so that R = 15/40 = 0.375. Contributions equal to 37.5% of salary are therefore necessary. This simple example illustrates the problems with defined benefit plans. Total contributions of employer and employee are, in practice, 15% or less, but much higher contributions are necessary to pay promised pensions with certainty.
答案中DB收入中的R，请问有相关公式吗？
