Question

Your cousin Joe at age 25 wants to plan for his retirement and estimates to retire at the age of 65. He already has $5000 in his savings that he received as a gift from his mother. He plans to save some of his income each year during his working years and he plans to increase his savings at a constant 5% each year.

He wants to be able to spend $100,000 for 20 years after his retirement and at the end he wants $300,000 savings to donate his favorite charity. Retirement spending must increase and cover 2% annual inflation as well.  

He expects to make 5% return on his savings during working years and 4% after retirement.

Assume cash flows occur at the end of the year.

Calculate the saving amount in the first year of working for Joe.

Answer 1

The retirement spending must cover the inflation rate as well, therefore the real rate of return during the retirement period is found to be

Real rate of return during the retirement period = 1.96%

The size of the withdrawl during the retirement period is calculated using the present value of annuity equation.

Size of withdrawl when Joe is 65 years = $ 1,778,388.86

When Joe is 25 years, the size of the withdrawl = $ 1,778,388.86 ( 1 + 0.05 )40  

Size of withdrawl when Joe is 25 years = 252612.4589

Using the present value of investment equation and present value of growing annuity equation, we can found out the saving amount in the first year of working for Joe.

when r = g, the present value of growing annuity equals nA, where n is the number of years and A is the annual amount.

  

where A is the saving amount in the first year of working for Joe

Solving for A, we get

A = $ 12595

Joe must save $ 12595 in the first year of working.