# You have just turned 22 years old. Now you must decide how much money to put into your retirement...

You have just turned 22 years old. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 6.6% per year. You cannot make withdrawals until you retire on your 65th birthday. After that, you can make withdrawals as you see fit. You decide that you will plan to live until 100 and work until you turn 65. You estimate that to live comfortably in retirement, you will need $110,000 per year, starting at the end of the first year of retirement and ending on your 100th birthday. You will contribute the same amount to the plan at the end of every year that you work. How much will you need to contribute each year to fund your retirement? ## Saving for Retirement: Saving for retirement is one of the most important financial decisions in life. Retirement is often financed through periodic contributions to a saving account during one's working age. A critical piece of information is the future value of the contributions near retirement. ## Answer and Explanation: The annual contribution is$6,991.13.

The annual contribution, denoted by {eq}M{/eq}, must be such that the future value of these contributions (which are an annuity), will have a future value that is equal to the present value of the post-retirement expenses.

To find the required contribution, we first compute the present value (at retirement time) of future expenses. Annual expense is 110,000, and there are (100 - 65) = 35 years of expenses. The value of these expenses at retirement time is:

• {eq}\displaystyle \frac{110,000*(1 - (1 + 6.5\%)^{-35})}{6.5\%} = 1,505,565.24 {/eq}

Between 22 and 65, there are 43 annual contributions. For the contribution to support the expenses, we must have:

• {eq}\displaystyle \frac{M*((1 + 6.5\%)^{43} - 1)}{6.5\%} = 1,505,565.24 {/eq}

which yields:

• {eq}M = 6,991.13 {/eq}