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Retirement worksheet

Grades 11–12 · CCSS HSA.SSE.B.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Current age: 32 years
- Retirement age: 75 years
- Plan for savings to last until age: 110 years
- Current retirement savings: $46,000
- Monthly contribution: $650
- Raise contributions each year by: 1%
- Return before retirement: 6% a year
- Return during retirement: 5.4% a year
- Inflation: 3% a year
- Yearly income you want in retirement: $62,500
- Yearly Social Security and pension income: $20,000
Find: Projected savings at age 75
Answer
2.
Problem 2.
- Current age: 29 years
- Retirement age: 75 years
- Plan for savings to last until age: 90 years
- Current retirement savings: $90,000
- Monthly contribution: $920
- Raise contributions each year by: 3%
- Return before retirement: 7% a year
- Return during retirement: 5.6% a year
- Inflation: 2% a year
- Yearly income you want in retirement: $76,000
- Yearly Social Security and pension income: $31,000
Find: Projected savings at age 75
Answer
3.
Problem 3.
- Current age: 36 years
- Retirement age: 50 years
- Plan for savings to last until age: 90 years
- Current retirement savings: $54,000
- Monthly contribution: $750
- Raise contributions each year by: 2%
- Return before retirement: 6% a year
- Return during retirement: 3.6% a year
- Inflation: 2% a year
- Yearly income you want in retirement: $65,000
- Yearly Social Security and pension income: $25,000
Find: Projected savings at age 50
Answer
4.
Problem 4.
- Current age: 28 years
- Retirement age: 60 years
- Plan for savings to last until age: 102 years
- Current retirement savings: $49,000
- Monthly contribution: $850
- Raise contributions each year by: 3%
- Return before retirement: 6% a year
- Return during retirement: 4.8% a year
- Inflation: 2.8% a year
- Yearly income you want in retirement: $54,000
- Yearly Social Security and pension income: $25,000
Find: Projected savings at age 60
Answer
5.
Problem 5.
- Current age: 24 years
- Retirement age: 80 years
- Plan for savings to last until age: 100 years
- Current retirement savings: $60,000
- Monthly contribution: $550
- Raise contributions each year by: 2%
- Return before retirement: 7% a year
- Return during retirement: 4% a year
- Inflation: 2.8% a year
- Yearly income you want in retirement: $70,000
- Yearly Social Security and pension income: $32,500
Find: Projected savings at age 80
Answer
6.
Problem 6.
- Current age: 35 years
- Retirement age: 73 years
- Plan for savings to last until age: 85 years
- Current retirement savings: $55,000
- Monthly contribution: $950
- Raise contributions each year by: 1%
- Return before retirement: 7% a year
- Return during retirement: 4.5% a year
- Inflation: 3.2% a year
- Yearly income you want in retirement: $76,000
- Yearly Social Security and pension income: $34,000
Find: Projected savings at age 73
Answer
7.
Problem 7.
- Current age: 32 years
- Retirement age: 68 years
- Plan for savings to last until age: 105 years
- Current retirement savings: $50,000
- Monthly contribution: $800
- Raise contributions each year by: 2%
- Return before retirement: 5% a year
- Return during retirement: 6% a year
- Inflation: 2.4% a year
- Yearly income you want in retirement: $80,000
- Yearly Social Security and pension income: $19,500
Find: Projected savings at age 68
Answer
8.
Problem 8.
- Current age: 38 years
- Retirement age: 85 years
- Plan for savings to last until age: 90 years
- Current retirement savings: $64,000
- Monthly contribution: $710
- Raise contributions each year by: 2%
- Return before retirement: 4% a year
- Return during retirement: 4.2% a year
- Inflation: 2.5% a year
- Yearly income you want in retirement: $50,000
- Yearly Social Security and pension income: $30,000
Find: Projected savings at age 85
Answer
9.
Problem 9.
- Current age: 33 years
- Retirement age: 74 years
- Plan for savings to last until age: 80 years
- Current retirement savings: $77,500
- Monthly contribution: $720
- Raise contributions each year by: 3%
- Return before retirement: 8% a year
- Return during retirement: 3.6% a year
- Inflation: 2.4% a year
- Yearly income you want in retirement: $75,000
- Yearly Social Security and pension income: $28,000
Find: Projected savings at age 74
Answer
10.
Problem 10.
- Current age: 32 years
- Retirement age: 70 years
- Plan for savings to last until age: 90 years
- Current retirement savings: $70,000
- Monthly contribution: $1,200
- Raise contributions each year by: 2%
- Return before retirement: 6% a year
- Return during retirement: 5.8% a year
- Inflation: 2.3% a year
- Yearly income you want in retirement: $55,000
- Yearly Social Security and pension income: $18,000
Find: Projected savings at age 70
Answer

Answer key: Retirement worksheet

1. Projected savings at age 75: $2,280,781.33
1. Count the years you have left to save before you retire
  $75 - 32$ $= 43$
2. Turn the 6% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00486755$
3. Grow what you have today, plus monthly deposits that rise 1% a year, one month at a time until age 75
  $savings at age 75$ $= $2,280,781.33$
4. Undo 43 years of 3% price rises to see what that would buy today
  $\frac{$2,280,781.33}{{(1 + 0.03)}^{43}}$ $= $639,857.09$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($62,500.00 - $20,000.00) \times {(1 + 0.03)}^{43}$ $= $151,491.96$
6. Find the savings you need on day one: enough to pay 35 years of monthly withdrawals that rise with prices, while the rest earns 5.4% a year
  $savings needed$ $= $3,594,754.64$
7. Compare that with what you're on track to have. The gap is your shortfall
  $$3,594,754.64 - $2,280,781.33$ $= $1,313,973.30$
8. Find the extra to save each month: divide the gap by what $1 a month grows to over 516 months
  $\frac{$1,313,973.30}{2,311.3175}$ $= $568.50$
9. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$2,280,781.33}{84.5825} + $20,000.00$ $= $46,965.18$
2. Projected savings at age 75: $7,312,443.10
1. Count the years you have left to save before you retire
  $75 - 29$ $= 46$
2. Turn the 7% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00565415$
3. Grow what you have today, plus monthly deposits that rise 3% a year, one month at a time until age 75
  $savings at age 75$ $= $7,312,443.10$
4. Undo 46 years of 2% price rises to see what that would buy today
  $\frac{$7,312,443.10}{{(1 + 0.02)}^{46}}$ $= $2,940,726.25$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($76,000.00 - $31,000.00) \times {(1 + 0.02)}^{46}$ $= $111,897.51$
6. Find the savings you need on day one: enough to pay 15 years of monthly withdrawals that rise with prices, while the rest earns 5.6% a year
  $savings needed$ $= $1,298,788.55$
7. Compare that with what you're on track to have. You're ahead of your goal by this much
  $$7,312,443.10 - $1,298,788.55$ $= $6,013,654.56$
8. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$7,312,443.10}{28.862} + $31,000.00$ $= $284,359.13$
3. Projected savings at age 50: $339,673.27
1. Count the years you have left to save before you retire
  $50 - 36$ $= 14$
2. Turn the 6% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00486755$
3. Grow what you have today, plus monthly deposits that rise 2% a year, one month at a time until age 50
  $savings at age 50$ $= $339,673.27$
4. Undo 14 years of 2% price rises to see what that would buy today
  $\frac{$339,673.27}{{(1 + 0.02)}^{14}}$ $= $257,429.89$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($65,000.00 - $25,000.00) \times {(1 + 0.02)}^{14}$ $= $52,779.15$
6. Find the savings you need on day one: enough to pay 40 years of monthly withdrawals that rise with prices, while the rest earns 3.6% a year
  $savings needed$ $= $1,558,404.42$
7. Compare that with what you're on track to have. The gap is your shortfall
  $$1,558,404.42 - $339,673.27$ $= $1,218,731.15$
8. Find the extra to save each month: divide the gap by what $1 a month grows to over 168 months
  $\frac{$1,218,731.15}{259.0428}$ $= $4,704.75$
9. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$339,673.27}{38.9601} + $25,000.00$ $= $33,718.49$
4. Projected savings at age 60: $1,670,719.94
1. Count the years you have left to save before you retire
  $60 - 28$ $= 32$
2. Turn the 6% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00486755$
3. Grow what you have today, plus monthly deposits that rise 3% a year, one month at a time until age 60
  $savings at age 60$ $= $1,670,719.94$
4. Undo 32 years of 2.8% price rises to see what that would buy today
  $\frac{$1,670,719.94}{{(1 + 0.028)}^{32}}$ $= $690,436.89$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($54,000.00 - $25,000.00) \times {(1 + 0.028)}^{32}$ $= $70,174.23$
6. Find the savings you need on day one: enough to pay 42 years of monthly withdrawals that rise with prices, while the rest earns 4.8% a year
  $savings needed$ $= $1,996,950.33$
7. Compare that with what you're on track to have. The gap is your shortfall
  $$1,996,950.33 - $1,670,719.94$ $= $326,230.39$
8. Find the extra to save each month: divide the gap by what $1 a month grows to over 384 months
  $\frac{$326,230.39}{1,120.3554}$ $= $291.18$
9. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$1,670,719.94}{68.8604} + $25,000.00$ $= $49,262.44$
5. Projected savings at age 80: $8,259,889.88
1. Count the years you have left to save before you retire
  $80 - 24$ $= 56$
2. Turn the 7% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00565415$
3. Grow what you have today, plus monthly deposits that rise 2% a year, one month at a time until age 80
  $savings at age 80$ $= $8,259,889.88$
4. Undo 56 years of 2.8% price rises to see what that would buy today
  $\frac{$8,259,889.88}{{(1 + 0.028)}^{56}}$ $= $1,759,380.75$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($70,000.00 - $32,500.00) \times {(1 + 0.028)}^{56}$ $= $176,053.92$
6. Find the savings you need on day one: enough to pay 20 years of monthly withdrawals that rise with prices, while the rest earns 4% a year
  $savings needed$ $= $3,104,461.51$
7. Compare that with what you're on track to have. You're ahead of your goal by this much
  $$8,259,889.88 - $3,104,461.51$ $= $5,155,428.37$
8. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$8,259,889.88}{82.7856} + $32,500.00$ $= $132,274.43$
6. Projected savings at age 73: $2,997,078.12
1. Count the years you have left to save before you retire
  $73 - 35$ $= 38$
2. Turn the 7% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00565415$
3. Grow what you have today, plus monthly deposits that rise 1% a year, one month at a time until age 73
  $savings at age 73$ $= $2,997,078.12$
4. Undo 38 years of 3.2% price rises to see what that would buy today
  $\frac{$2,997,078.12}{{(1 + 0.032)}^{38}}$ $= $905,460.62$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($76,000.00 - $34,000.00) \times {(1 + 0.032)}^{38}$ $= $139,020.16$
6. Find the savings you need on day one: enough to pay 12 years of monthly withdrawals that rise with prices, while the rest earns 4.5% a year
  $savings needed$ $= $1,527,694.03$
7. Compare that with what you're on track to have. You're ahead of your goal by this much
  $$2,997,078.12 - $1,527,694.03$ $= $1,469,384.09$
8. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$2,997,078.12}{36.3737} + $34,000.00$ $= $116,396.92$
7. Projected savings at age 68: $1,517,479.79
1. Count the years you have left to save before you retire
  $68 - 32$ $= 36$
2. Turn the 5% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00407412$
3. Grow what you have today, plus monthly deposits that rise 2% a year, one month at a time until age 68
  $savings at age 68$ $= $1,517,479.79$
4. Undo 36 years of 2.4% price rises to see what that would buy today
  $\frac{$1,517,479.79}{{(1 + 0.024)}^{36}}$ $= $646,136.80$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($80,000.00 - $19,500.00) \times {(1 + 0.024)}^{36}$ $= $142,086.83$
6. Find the savings you need on day one: enough to pay 37 years of monthly withdrawals that rise with prices, while the rest earns 6% a year
  $savings needed$ $= $2,939,496.29$
7. Compare that with what you're on track to have. The gap is your shortfall
  $$2,939,496.29 - $1,517,479.79$ $= $1,422,016.49$
8. Find the extra to save each month: divide the gap by what $1 a month grows to over 432 months
  $\frac{$1,422,016.49}{1,176.1587}$ $= $1,209.03$
9. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$1,517,479.79}{48.5867} + $19,500.00$ $= $50,732.40$
8. Projected savings at age 85: $2,044,571.48
1. Count the years you have left to save before you retire
  $85 - 38$ $= 47$
2. Turn the 4% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00327374$
3. Grow what you have today, plus monthly deposits that rise 2% a year, one month at a time until age 85
  $savings at age 85$ $= $2,044,571.48$
4. Undo 47 years of 2.5% price rises to see what that would buy today
  $\frac{$2,044,571.48}{{(1 + 0.025)}^{47}}$ $= $640,590.69$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($50,000.00 - $30,000.00) \times {(1 + 0.025)}^{47}$ $= $63,833.94$
6. Find the savings you need on day one: enough to pay 5 years of monthly withdrawals that rise with prices, while the rest earns 4.2% a year
  $savings needed$ $= $303,174.39$
7. Compare that with what you're on track to have. You're ahead of your goal by this much
  $$2,044,571.48 - $303,174.39$ $= $1,741,397.08$
8. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$2,044,571.48}{15.1587} + $30,000.00$ $= $164,877.58$
9. Projected savings at age 74: $5,417,669.26
1. Count the years you have left to save before you retire
  $74 - 33$ $= 41$
2. Turn the 8% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00643403$
3. Grow what you have today, plus monthly deposits that rise 3% a year, one month at a time until age 74
  $savings at age 74$ $= $5,417,669.26$
4. Undo 41 years of 2.4% price rises to see what that would buy today
  $\frac{$5,417,669.26}{{(1 + 0.024)}^{41}}$ $= $2,048,869.35$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($75,000.00 - $28,000.00) \times {(1 + 0.024)}^{41}$ $= $124,278.52$
6. Find the savings you need on day one: enough to pay 6 years of monthly withdrawals that rise with prices, while the rest earns 3.6% a year
  $savings needed$ $= $712,797.86$
7. Compare that with what you're on track to have. You're ahead of your goal by this much
  $$5,417,669.26 - $712,797.86$ $= $4,704,871.40$
8. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$5,417,669.26}{15.1659} + $28,000.00$ $= $385,226.74$
10. Projected savings at age 70: $3,241,184.91
1. Count the years you have left to save before you retire
  $70 - 32$ $= 38$
2. Turn the 6% yearly return into a monthly rate i, because your savings grow every month
  $i$ $= 0.00486755$
3. Grow what you have today, plus monthly deposits that rise 2% a year, one month at a time until age 70
  $savings at age 70$ $= $3,241,184.91$
4. Undo 38 years of 2.3% price rises to see what that would buy today
  $\frac{$3,241,184.91}{{(1 + 0.023)}^{38}}$ $= $1,365,934.04$
5. Find what your savings must pay each year: your income goal minus Social Security and pensions, raised for price rises until you retire
  $($55,000.00 - $18,000.00) \times {(1 + 0.023)}^{38}$ $= $87,796.22$
6. Find the savings you need on day one: enough to pay 20 years of monthly withdrawals that rise with prices, while the rest earns 5.8% a year
  $savings needed$ $= $1,266,733.94$
7. Compare that with what you're on track to have. You're ahead of your goal by this much
  $$3,241,184.91 - $1,266,733.94$ $= $1,974,450.97$
8. Find the yearly income you could afford in today's dollars: what your savings can pay, plus Social Security and pensions
  $\frac{$3,241,184.91}{34.2361} + $18,000.00$ $= $112,671.69$