Exercises: Sources of Retirement Income

Classify each as a source of retirement income provided by the government, by an employer, by personal investments, or by work:

(a) Social Security benefits;

(b) a 401(k) with employer contributions;

(c) a traditional pension;

(d) a Roth IRA the person opened;

(e) a part-time job after age 65.

Jayden earns $\$2{,}000$ per month. His employer matches his 401(k) contributions dollar for dollar up to 3% of his pay. He contributes 3% each month. Calculate his contribution, the employer's match, and the total deposited that month.

Suppose the average retired worker receives about $\$1{,}900$ per month from Social Security (a rounded figure). Calculate the yearly amount. Is this likely to cover all expenses for most retirees? Explain briefly.

Priya's final salary before retirement is $\$60{,}000$ a year. Suppose Social Security replaces about 40% of that income, and she wants to replace 80% in total.

(a) Calculate her yearly Social Security income and her yearly income goal.

(b) Calculate the yearly gap that must come from other sources.

(c) If she plans to withdraw 4% of her savings each year, how large must her savings be to cover the gap?

Valeria earns $\$48{,}000$ a year and compares two employers.

• Plan A: matches 100% of contributions up to 4% of salary.

• Plan B: matches 50% of contributions up to 6% of salary.

(a) Calculate the employer contribution under each plan if she contributes 4% of salary.

(b) Calculate the employer contribution under each plan if she contributes 8% of salary.

(c) Explain which plan is better and why contributing at least up to the match limit matters.

Use the Rule of 72. An investment earns 8% a year, so it doubles about every 72 ÷ 8 = 9 years. Emma invests $\$5{,}000$ at age 25 and does not add more. Her friend Marcus invests $\$5{,}000$ at age 34 and does not add more. Both plan to retire at 61.

(a) How many doublings does each investment have?

(b) Estimate the value at age 61 for each.

(c) Explain what this shows about personal investments as a retirement source.

Emma is 65. Her expected Social Security benefit is $\$1{,}900$ per month, and she has no pension. She has $\$420{,}000$ in a 401(k) and plans to withdraw 4% a year. Her monthly expenses are $\$4{,}200$. She can also work part time for 5 years and earn $\$800$ per month.

(a) Calculate her monthly income from the 401(k) and her total monthly income without work.

(b) Calculate the monthly shortfall with and without the part-time job.

(c) Evaluate two ways she could close the remaining gap, such as reducing expenses, working longer, or delaying benefits.

Jayden earns $\$50{,}000$. His employer matches 50% of his 401(k) contributions, up to 6% of salary. Consider contribution rates of 0%, 3%, 6%, and 10%.

(a) For each rate, calculate his contribution, the employer match, and the total deposited per year.

(b) Calculate the "instant return" (employer match divided by his contribution) at 3% and at 6%.

(c) Calculate the extra employer money gained by moving from 6% to 10%.

(d) Argue how he should prioritize contributions relative to other goals, such as paying off a high-interest credit card.