You just accepted a job after graduating from business school. Since it is never too early to

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Question:

You just accepted a job after graduating from business school. Since it is never too early to start thinking about saving for retirement you compute how much income you will have at retirement. You are currently 30 years old and you plan to retire in 35 years. Your initial salary is $100,000 (paid annually at the end of the year) and you expect that it will grow at 6% per year until you retire. Your company allows you to save in a 401(k) retirement account. Your company will match your contribution by 50%. For example, if you save 2% your total contribution including the employer match is 3%; if you save 4%, your total contribution is 6%; if you save 8%, your total contribution is 12%; and so on. To allow you a comfortable standard of living during retirement, you want to cover 75% of your income during the last year prior to retirement. You also expect to obtain social security income which would replace 25% of your income during the last year prior to retirement. Thus, your savings in the company's 401(k) account should accumulate to a sufficient amount to enable you to cover in the first year of retirement 50% of your last pre-retirement salary.

For example, if your final salary is $700,000, then you would need to withdraw $350,000 from your 401(k) account at the end of your first retirement year. Subsequently, you expect your withdrawals in retirement and your social security income to increase at the rate of inflation, which you anticipate to amount to 3% per year. Since you are in excellent health, you anticipate to live until age 95 (i.e., you anticipate to make 30 annual withdrawals from your 401(k) account). You decide to invest in a relatively conservative balanced portfolio that includes 50% stocks and 50% bonds and that has an expected return of 8%.

Which proportion of your income do you need to contribute to the retirement account to ensure that you can meet your future financial needs in retirement? Explain in detail the various steps of your computations.