Question

Retirement plans, are divided into two phases: the payments periods and the pension periods. The participants pay an ordinary annuity during the payment period (say for n₁ years) where upon retirement they are paid an annual retirement pension. Assume the average pension period is n₂ years. If a retirement organization believes that the participants should pay one tenth of as much as they should get as pension every year, what is the value of n₁ and n₂ that keeps the cash flow of the two periods balanced at a discount rate of 10%. Suppose that the sum of payment and pension periods is 50 years.

Answer 1

As per the given data = n1 + n2 = 50

Let us suppose that the pensioner gets and annual pension of X

Therefore, his annual premium = X/10

Now, since discount rate of 10% is applicable = 10% of X/10

                                                                                  = 0.X

Now, if n1 + n2 = 50

Therefore = n1 = 50-n2

                    = n1 = 50 – 0.X

                  & n2 = 50- (50-0.X)

                            = 2500- 5X

Hence n1 = 50 – 0.X & n2 = 2500- 5X