解决方案

假设情景：

You are planning for retirement at age 65 based on the provided fictional financial situation.

问题集 1

问题 1A：

Calculate the total amount of savings needed by age 65 to meet the desired retirement income. Consider the expected Social Security or public pension benefit in your calculations.

解决方案:

Desired Retirement Income Calculation:

• Current Salary: $70,000
• Desired Retirement Income: 80% of $70,000 = $56,000 annually
• Monthly Retirement Income: $56,000 / 12 = $4,666.67

\(\textbf{Monthly Retirement Income Calculation:}\)

\[ \displaystyle \text{Monthly Retirement Income} = \frac{\$56,000}{12} = \$4,666.67 \]

\（\textbf{图例：}\）

\(\text{Monthly Retirement Income}\) = Monthly retirement income

\(\$56,000\) = Annual retirement income

\(12\) = Number of months in a year

Retirement Income from Social Security/Public Pension:

• Social Security Benefit (USA): $1,500 monthly
• Public Pension Benefit (Canada): $1,200 monthly

Additional Monthly Income Needed:

• USA: $4,666.67 – $1,500 = $3,166.67
• Canada: $4,666.67 – $1,200 = $3,466.67

Annual Additional Income Needed:

• USA: $3,166.67 * 12 = $38,000
• Canada: $3,466.67 * 12 = $41,600

Total Savings Needed:

• USA: $38,000 / 0.05 = $760,000
• Canada: $41,600 / 0.05 = $832,000

问题 1B：

Develop a savings plan to reach the required retirement savings goal. Include annual contributions, employer matches, and expected investment growth.

解决方案:

Savings Plan Calculation:

1. Annual Savings:
   • Salary: $70,000
   • Annual Savings Rate: 10% of $70,000 = $7,000
   • Employer 401(k) Match: 50% of contributions up to 6% of salary = $2,100
   • Total Annual Savings: $7,000 + $2,100 = $9,100
2. Investment Growth Calculation:
   • Current Savings: $20,000
   • Annual Contribution: $9,100
   • Investment Growth Rate: 5%

Future Value Calculation:

𝐹𝑉=𝑃𝑉×(1+𝑟)𝑛+𝑃𝑀𝑇×((1+𝑟)𝑛−1)𝑟
\(\textbf{Future Value (FV) Formula:}\)

\[ \displaystyle FV = PV \times (1 + r)^n + PMT \times \left( \frac{(1 + r)^n – 1}{r} \right) \]

\（\textbf{图例：}\）

\(FV\) = Future Value

\(PV\) = Present Value

\(r\) = Interest rate

\(n\) = Number of periods

\(PMT\) = Regular payment

​

Where:

• PV = $20,000
• PMT = $9,100
• 𝑟=0.05
• r=0.05
• 𝑛=35
• n=35 (years until retirement)

\[ \displaystyle FV = 20,000 \times (1 + 0.05)^{35} + \frac{9,100 \times ((1 + 0.05)^{35} – 1)}{0.05} \approx \$876,474.15 \]

\（\textbf{图例：}\）

\(FV\) = Future Value

\(20,000\) = Present Value (initial investment)

\(0.05\) = Interest rate (5%)

\(35\) = Number of periods (years)

\(9,100\) = Regular annual payment

Comparison to Goal:

• USA: $876,474.15 (sufficient to meet $760,000 goal)
• Canada: $876,474.15 (sufficient to meet $832,000 goal)

问题 1C：

Explain the role of different sources of retirement income in your plan, including personal savings, employer-sponsored plans, and Social Security or public pensions.

解决方案:

Role of Retirement Income Sources:

1. Personal Savings:
   • Description: Contributions to retirement accounts such as 401(k), IRA, or RRSP.
   • Role: Primary source of retirement income to cover living expenses beyond Social Security or public pensions.
2. Employer-Sponsored Plans:
   • Description: 401(k) plans in the USA, pension plans, or group RRSPs in Canada.
   • Role: Employer contributions and matches enhance retirement savings, reducing the individual’s financial burden.
3. Social Security/Public Pensions:
   • Description: Government-provided benefits based on work history and earnings.
   • Role: Provides a foundational income stream to cover basic living expenses in retirement.

Integration in Plan:

• Balance Contributions: Ensure a mix of personal savings and employer-sponsored plans to maximize tax advantages and employer matches.
• Leverage Benefits: Rely on Social Security or public pensions as a stable income source while using personal savings for discretionary spending and unforeseen expenses.