I need help with finding an appropriate formula to use in this scenario. I am trying to solve the famous 4 percent withdrawal problem. Here's the problem statement:
On a form, user enters his retirement accumulated savings amount and his retirement age. The income he will receive is determined as follows:
If years in retirement is > 30 years, then his starting retirement income is 3.5 percent of his accumulated savings.
If years in retirement is < 30 and > 20 years, then his starting retirement income is 4 percent of his accumulated savings.
If years in retirement is < 20 years, then his starting retirement income is 5 percent of his accumulated savings.
We assume that the user will live 90 years. The issue with the above scenario is that for the same savings amount, the retirement income jumps unnaturally for border cases. For example, if the user retires at 69, his income is 23K / year, whereas if he retires one year later, he can expect an income of 30K / year. This is because withdrawal percent jumps from 4 to 5 percent. What is the best approach to smoothen / average the withdrawal percentage for all the above scenarios and still retain the essence of the above formula?