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Rent vs Buy worksheet

Grades 11–12 · CCSS HSA.SSE.B.4, HSF.LE.A.2

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

1.
Problem 1.
- Monthly rent: $2,000
- Rent increase: 3% per year
- Home price: $450,000
- Down payment: 15% of price
- Mortgage rate: 5.5% per year
- Mortgage term: 15 years
- Buying closing costs: 2% of price
- Selling costs: 6% of sale price
- Property tax: 1.1% of value per year
- Home insurance: $2,300 per year
- Maintenance and repairs: 1% of value per year
- HOA dues: $0 per month
- Home price growth: 3% per year
- Investment return: 3% per year
- Years you expect to stay: 9 years
Find: Buying minus renting after 9 years
Answer
2.
Problem 2.
- Monthly rent: $2,000
- Rent increase: 4% per year
- Home price: $350,000
- Down payment: 22% of price
- Mortgage rate: 6.5% per year
- Mortgage term: 15 years
- Buying closing costs: 3% of price
- Selling costs: 6% of sale price
- Property tax: 1.1% of value per year
- Home insurance: $1,300 per year
- Maintenance and repairs: 1% of value per year
- HOA dues: $0 per month
- Home price growth: 2% per year
- Investment return: 5% per year
- Years you expect to stay: 6 years
Find: Buying minus renting after 6 years
Answer
3.
Problem 3.
- Monthly rent: $2,750
- Rent increase: 2% per year
- Home price: $460,000
- Down payment: 24% of price
- Mortgage rate: 4.2% per year
- Mortgage term: 20 years
- Buying closing costs: 3% of price
- Selling costs: 8% of sale price
- Property tax: 0.9% of value per year
- Home insurance: $2,200 per year
- Maintenance and repairs: 1% of value per year
- HOA dues: $0 per month
- Home price growth: 3% per year
- Investment return: 6% per year
- Years you expect to stay: 6 years
Find: Buying minus renting after 6 years
Answer
4.
Problem 4.
- Monthly rent: $1,800
- Rent increase: 3% per year
- Home price: $450,000
- Down payment: 20% of price
- Mortgage rate: 6.1% per year
- Mortgage term: 30 years
- Buying closing costs: 3% of price
- Selling costs: 7% of sale price
- Property tax: 0.9% of value per year
- Home insurance: $1,900 per year
- Maintenance and repairs: 2% of value per year
- HOA dues: $0 per month
- Home price growth: 3% per year
- Investment return: 5% per year
- Years you expect to stay: 8 years
Find: Buying minus renting after 8 years
Answer
5.
Problem 5.
- Monthly rent: $1,700
- Rent increase: 3% per year
- Home price: $275,000
- Down payment: 24% of price
- Mortgage rate: 7.5% per year
- Mortgage term: 15 years
- Buying closing costs: 4% of price
- Selling costs: 5% of sale price
- Property tax: 0.9% of value per year
- Home insurance: $2,300 per year
- Maintenance and repairs: 1% of value per year
- HOA dues: $0 per month
- Home price growth: 3% per year
- Investment return: 6% per year
- Years you expect to stay: 9 years
Find: Buying minus renting after 9 years
Answer
6.
Problem 6.
- Monthly rent: $2,000
- Rent increase: 3% per year
- Home price: $325,000
- Down payment: 15% of price
- Mortgage rate: 8% per year
- Mortgage term: 20 years
- Buying closing costs: 3% of price
- Selling costs: 7% of sale price
- Property tax: 1.1% of value per year
- Home insurance: $2,250 per year
- Maintenance and repairs: 1% of value per year
- HOA dues: $0 per month
- Home price growth: 4% per year
- Investment return: 5% per year
- Years you expect to stay: 6 years
Find: Buying minus renting after 6 years
Answer
7.
Problem 7.
- Monthly rent: $2,050
- Rent increase: 2% per year
- Home price: $390,000
- Down payment: 24% of price
- Mortgage rate: 6.5% per year
- Mortgage term: 30 years
- Buying closing costs: 3% of price
- Selling costs: 7% of sale price
- Property tax: 1.1% of value per year
- Home insurance: $1,500 per year
- Maintenance and repairs: 2% of value per year
- HOA dues: $0 per month
- Home price growth: 3% per year
- Investment return: 6% per year
- Years you expect to stay: 5 years
Find: Buying minus renting after 5 years
Answer
8.
Problem 8.
- Monthly rent: $1,800
- Rent increase: 2% per year
- Home price: $400,000
- Down payment: 18% of price
- Mortgage rate: 4.8% per year
- Mortgage term: 20 years
- Buying closing costs: 4% of price
- Selling costs: 6% of sale price
- Property tax: 1.2% of value per year
- Home insurance: $1,500 per year
- Maintenance and repairs: 2% of value per year
- HOA dues: $0 per month
- Home price growth: 3% per year
- Investment return: 6% per year
- Years you expect to stay: 9 years
Find: Buying minus renting after 9 years
Answer
9.
Problem 9.
- Monthly rent: $1,700
- Rent increase: 3% per year
- Home price: $450,000
- Down payment: 22% of price
- Mortgage rate: 6.5% per year
- Mortgage term: 30 years
- Buying closing costs: 3% of price
- Selling costs: 5% of sale price
- Property tax: 1% of value per year
- Home insurance: $2,400 per year
- Maintenance and repairs: 1% of value per year
- HOA dues: $0 per month
- Home price growth: 3% per year
- Investment return: 7% per year
- Years you expect to stay: 5 years
Find: Buying minus renting after 5 years
Answer
10.
Problem 10.
- Monthly rent: $1,450
- Rent increase: 3% per year
- Home price: $500,000
- Down payment: 20% of price
- Mortgage rate: 5.6% per year
- Mortgage term: 30 years
- Buying closing costs: 4% of price
- Selling costs: 9% of sale price
- Property tax: 1.1% of value per year
- Home insurance: $1,600 per year
- Maintenance and repairs: 1% of value per year
- HOA dues: $0 per month
- Home price growth: 2% per year
- Investment return: 4% per year
- Years you expect to stay: 7 years
Find: Buying minus renting after 7 years
Answer

Answer key: Rent vs Buy worksheet

1. Buying minus renting after 9 years: $19,057.04
1. Loan amount: the price minus the down payment
  $$450,000.00 - $67,500.00$ $= $382,500.00$
2. Work out the monthly mortgage payment over 180 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$382,500.00 \times 0.00458333}{1 - {(1 + 0.00458333)}^{−180}}$ $= $3,125.34$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$3,125.34 + \frac{$450,000.00 \times 1.1%}{12} + \frac{$2,300.00}{12} + \frac{$450,000.00 \times 1%}{12} + $0.00$ $= $4,104.51$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$67,500.00 + $450,000.00 \times 2%$ $= $76,500.00$
5. Grow the home's value by 3% a year for 9 years
  $$450,000.00 \times {(1 + 3%)}^{9}$ $= $587,147.93$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$587,147.93 \times (1 - 6%) - $191,294.27 + $0.00$ $= $360,624.78$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 3% a year for 9 years
  $renter's investments$ $= $341,567.74$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$360,624.78 - $341,567.74$ $= $19,057.04$
2. Buying minus renting after 6 years: -$18,437.66
1. Loan amount: the price minus the down payment
  $$350,000.00 - $77,000.00$ $= $273,000.00$
2. Work out the monthly mortgage payment over 180 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$273,000.00 \times 0.00541667}{1 - {(1 + 0.00541667)}^{−180}}$ $= $2,378.12$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$2,378.12 + \frac{$350,000.00 \times 1.1%}{12} + \frac{$1,300.00}{12} + \frac{$350,000.00 \times 1%}{12} + $0.00$ $= $3,098.96$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$77,000.00 + $350,000.00 \times 3%$ $= $87,500.00$
5. Grow the home's value by 2% a year for 6 years
  $$350,000.00 \times {(1 + 2%)}^{6}$ $= $394,156.85$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$394,156.85 \times (1 - 6%) - $194,060.97 + $0.00$ $= $176,446.46$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 5% a year for 6 years
  $renter's investments$ $= $194,884.12$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$176,446.46 - $194,884.12$ $= −$18,437.66$
3. Buying minus renting after 6 years: $35,187.21
1. Loan amount: the price minus the down payment
  $$460,000.00 - $110,400.00$ $= $349,600.00$
2. Work out the monthly mortgage payment over 240 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$349,600.00 \times 0.0035}{1 - {(1 + 0.0035)}^{−240}}$ $= $2,155.53$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$2,155.53 + \frac{$460,000.00 \times 0.9%}{12} + \frac{$2,200.00}{12} + \frac{$460,000.00 \times 1%}{12} + $0.00$ $= $3,067.20$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$110,400.00 + $460,000.00 \times 3%$ $= $124,200.00$
5. Grow the home's value by 3% a year for 6 years
  $$460,000.00 \times {(1 + 3%)}^{6}$ $= $549,264.06$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$549,264.06 \times (1 - 8%) - $273,439.89 + $0.00$ $= $231,883.04$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 6% a year for 6 years
  $renter's investments$ $= $196,695.84$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$231,883.04 - $196,695.84$ $= $35,187.21$
4. Buying minus renting after 8 years: -$121,510.72
1. Loan amount: the price minus the down payment
  $$450,000.00 - $90,000.00$ $= $360,000.00$
2. Work out the monthly mortgage payment over 360 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$360,000.00 \times 0.00508333}{1 - {(1 + 0.00508333)}^{−360}}$ $= $2,181.58$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$2,181.58 + \frac{$450,000.00 \times 0.9%}{12} + \frac{$1,900.00}{12} + \frac{$450,000.00 \times 2%}{12} + $0.00$ $= $3,427.41$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$90,000.00 + $450,000.00 \times 3%$ $= $103,500.00$
5. Grow the home's value by 3% a year for 8 years
  $$450,000.00 \times {(1 + 3%)}^{8}$ $= $570,046.54$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$570,046.54 \times (1 - 7%) - $316,631.54 + $0.00$ $= $213,511.73$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 5% a year for 8 years
  $renter's investments$ $= $335,022.46$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$213,511.73 - $335,022.46$ $= −$121,510.72$
5. Buying minus renting after 9 years: -$2,967.48
1. Loan amount: the price minus the down payment
  $$275,000.00 - $66,000.00$ $= $209,000.00$
2. Work out the monthly mortgage payment over 180 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$209,000.00 \times 0.00625}{1 - {(1 + 0.00625)}^{−180}}$ $= $1,937.46$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$1,937.46 + \frac{$275,000.00 \times 0.9%}{12} + \frac{$2,300.00}{12} + \frac{$275,000.00 \times 1%}{12} + $0.00$ $= $2,564.54$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$66,000.00 + $275,000.00 \times 4%$ $= $77,000.00$
5. Grow the home's value by 3% a year for 9 years
  $$275,000.00 \times {(1 + 3%)}^{9}$ $= $358,812.63$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$358,812.63 \times (1 - 5%) - $112,055.71 + $0.00$ $= $228,816.28$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 6% a year for 9 years
  $renter's investments$ $= $231,783.77$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$228,816.28 - $231,783.77$ $= −$2,967.48$
6. Buying minus renting after 6 years: -$10,543.99
1. Loan amount: the price minus the down payment
  $$325,000.00 - $48,750.00$ $= $276,250.00$
2. Work out the monthly mortgage payment over 240 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$276,250.00 \times 0.00666667}{1 - {(1 + 0.00666667)}^{−240}}$ $= $2,310.67$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$2,310.67 + \frac{$325,000.00 \times 1.1%}{12} + \frac{$2,250.00}{12} + \frac{$325,000.00 \times 1%}{12} + $0.00$ $= $3,066.92$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$48,750.00 + $325,000.00 \times 3%$ $= $58,500.00$
5. Grow the home's value by 4% a year for 6 years
  $$325,000.00 \times {(1 + 4%)}^{6}$ $= $411,228.68$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$411,228.68 \times (1 - 7%) - $233,090.21 + $0.00$ $= $149,352.46$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 5% a year for 6 years
  $renter's investments$ $= $159,896.45$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$149,352.46 - $159,896.45$ $= −$10,543.99$
7. Buying minus renting after 5 years: -$62,935.70
1. Loan amount: the price minus the down payment
  $$390,000.00 - $93,600.00$ $= $296,400.00$
2. Work out the monthly mortgage payment over 360 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$296,400.00 \times 0.00541667}{1 - {(1 + 0.00541667)}^{−360}}$ $= $1,873.45$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$1,873.45 + \frac{$390,000.00 \times 1.1%}{12} + \frac{$1,500.00}{12} + \frac{$390,000.00 \times 2%}{12} + $0.00$ $= $3,005.95$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$93,600.00 + $390,000.00 \times 3%$ $= $105,300.00$
5. Grow the home's value by 3% a year for 5 years
  $$390,000.00 \times {(1 + 3%)}^{5}$ $= $452,116.89$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$452,116.89 \times (1 - 7%) - $277,462.94 + $0.00$ $= $143,005.77$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 6% a year for 5 years
  $renter's investments$ $= $205,941.47$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$143,005.77 - $205,941.47$ $= −$62,935.70$
8. Buying minus renting after 9 years: -$89,633.21
1. Loan amount: the price minus the down payment
  $$400,000.00 - $72,000.00$ $= $328,000.00$
2. Work out the monthly mortgage payment over 240 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$328,000.00 \times 0.004}{1 - {(1 + 0.004)}^{−240}}$ $= $2,128.58$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$2,128.58 + \frac{$400,000.00 \times 1.2%}{12} + \frac{$1,500.00}{12} + \frac{$400,000.00 \times 2%}{12} + $0.00$ $= $3,320.25$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$72,000.00 + $400,000.00 \times 4%$ $= $88,000.00$
5. Grow the home's value by 3% a year for 9 years
  $$400,000.00 \times {(1 + 3%)}^{9}$ $= $521,909.27$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$521,909.27 \times (1 - 6%) - $217,964.07 + $0.00$ $= $272,630.65$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 6% a year for 9 years
  $renter's investments$ $= $362,263.86$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$272,630.65 - $362,263.86$ $= −$89,633.21$
9. Buying minus renting after 5 years: -$91,431.87
1. Loan amount: the price minus the down payment
  $$450,000.00 - $99,000.00$ $= $351,000.00$
2. Work out the monthly mortgage payment over 360 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$351,000.00 \times 0.00541667}{1 - {(1 + 0.00541667)}^{−360}}$ $= $2,218.56$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$2,218.56 + \frac{$450,000.00 \times 1%}{12} + \frac{$2,400.00}{12} + \frac{$450,000.00 \times 1%}{12} + $0.00$ $= $3,168.56$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$99,000.00 + $450,000.00 \times 3%$ $= $112,500.00$
5. Grow the home's value by 3% a year for 5 years
  $$450,000.00 \times {(1 + 3%)}^{5}$ $= $521,673.33$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$521,673.33 \times (1 - 5%) - $328,574.53 + $0.00$ $= $167,015.14$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 7% a year for 5 years
  $renter's investments$ $= $258,447.01$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$167,015.14 - $258,447.01$ $= −$91,431.87$
10. Buying minus renting after 7 years: -$162,606.18
1. Loan amount: the price minus the down payment
  $$500,000.00 - $100,000.00$ $= $400,000.00$
2. Work out the monthly mortgage payment over 360 months. L is the loan and i is the monthly rate (the yearly rate ÷ 12): L × i ÷ (1 − (1 + i)^−n)
  $\frac{$400,000.00 \times 0.00466667}{1 - {(1 + 0.00466667)}^{−360}}$ $= $2,296.32$
3. Add up the first month of owning: mortgage, property tax, insurance, maintenance and HOA. This is what you compare with rent
  $$2,296.32 + \frac{$500,000.00 \times 1.1%}{12} + \frac{$1,600.00}{12} + \frac{$500,000.00 \times 1%}{12} + $0.00$ $= $3,304.65$
4. The renter invests what the buyer paid up front: the down payment plus buying costs
  $$100,000.00 + $500,000.00 \times 4%$ $= $120,000.00$
5. Grow the home's value by 2% a year for 7 years
  $$500,000.00 \times {(1 + 2%)}^{7}$ $= $574,342.83$
6. Find the buyer's net worth: sell the home, pay the selling costs and the loan, then add anything the buyer invested
  $$574,342.83 \times (1 - 9%) - $355,937.42 + $0.00$ $= $166,714.55$
7. Renter's net worth: the up-front money plus each month's difference in costs, grown at 4% a year for 7 years
  $renter's investments$ $= $329,320.74$
8. Advantage of buying: the buyer's net worth minus the renter's (negative means renting comes out ahead)
  $$166,714.55 - $329,320.74$ $= −$162,606.18$