Ryan Ripley is celebrating his 25th birthday today by accepting his first job offer as a software engineer with a local manufacturing firm since graduating college about 6 months ago. Ryan will be paid a starting salary of $30,655.68. His salary will be paid in annual installments with his first payment coming 1 year from today. Ryan plans to stay in this job for 41 years, such that he will receive his 41st and final salary payment on his 66th birthday. He expects to receive an annual raise of 3%. (Note that his first payment is already set, so he will receive 40 annual raises to his income.)

Ryan has just completed a meeting with his employer’s benefits counselor as part of the on-boarding process and, thus, has some important decisions regarding benefit plan selection. In particular, he is attempting to determine how best to handle his employer’s 401(k) plan. Following the advice of his benefits counselor, Ryan believes that, in retirement, he will want to target a 70% income replacement rate. That is, his first withdrawal from his 401(k) plan, which will occur on his 67th birthday (1 year after his final salary payment), should be equal to 70% of his final salary payment. Ryan wants to plan for a 30-year retirement, indicating that his last withdrawal should come on his 96th birthday. He also wants to be able to increase the size of his withdrawal by 2% per year so that his income keeps pace with increases in the cost of living.

Ryan is trying to determine how much of his annual salary he should set aside in his 401(k) plan each year to satisfy his retirement goals. Based off of some of the information gathered in his benefits meeting, he expects to earn a return of 7% per year on his 401(k) balance while working, and 5% per year once retired. Ryan does not have any interest in leaving any money to his heirs and, so, wants his final withdrawal from his retirement account to leave the account balance at zero. To work out what percentage of his salary to contribute to his 401(k) plan, Ryan has drawn up a list of questions to address. Since he isn’t terribly familiar with financial concepts, Ryan has asked for your help in addressing these questions. (Ignore any tax effects.)

What level of income will Ryan need in his first year of retirement? (That is, how large will that first withdrawal on his 67th birthday need to be?)

How much will Ryan need to have accumulated in his retirement account as of the end of his 41 first year (i.e. by his 66th birthday) working with the company in order to generate this level of income?

How much would Ryan have to deposit into his retirement account today (age 25) in order to fully fund his retirement goals if he were to make no subsequent deposits?

Realizing that he doesn’t have this much to deposit in a single lumps-sum today, Ryan wants to work out how much of each annual paycheck he would have to contribute to his retirement plan to fund his retirement goals. Assuming that he contributes a fixed percentage of his annual salary to his retirement account every year, what dollar amount would the first year’s contribution have to be?

What percentage of his income does Ryan need to set his contribution rate to?