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Motorcycle Loan 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.
- Motorcycle price: $19,000
- Down payment: $1,600
- Trade-in value: $850
- Sales tax rate: 6%
- Sales tax is charged on: The price minus the trade-in
- Sales tax is: Rolled into the loan
- Interest rate (APR): 8.5%
- Loan term: 24 months
- Insurance per year: $675
- Riding gear: $1,200
- Months you ride each year: 8
Find: Monthly payment
Answer
2.
Problem 2.
- Motorcycle price: $13,000
- Down payment: $1,300
- Trade-in value: $650
- Sales tax rate: 9%
- Sales tax is charged on: The price minus the trade-in
- Sales tax is: Rolled into the loan
- Interest rate (APR): 9%
- Loan term: 60 months
- Insurance per year: $800
- Riding gear: $1,000
- Months you ride each year: 11
Find: Monthly payment
Answer
3.
Problem 3.
- Motorcycle price: $17,000
- Down payment: $1,200
- Trade-in value: $1,075
- Sales tax rate: 8%
- Sales tax is charged on: The full price
- Sales tax is: Paid up front
- Interest rate (APR): 9%
- Loan term: 48 months
- Insurance per year: $500
- Riding gear: $1,000
- Months you ride each year: 7
Find: Monthly payment
Answer
4.
Problem 4.
- Motorcycle price: $21,500
- Down payment: $1,350
- Trade-in value: $1,050
- Sales tax rate: 10%
- Sales tax is charged on: The price minus the trade-in
- Sales tax is: Rolled into the loan
- Interest rate (APR): 6.5%
- Loan term: 36 months
- Insurance per year: $750
- Riding gear: $1,200
- Months you ride each year: 6
Find: Monthly payment
Answer
5.
Problem 5.
- Motorcycle price: $9,000
- Down payment: $1,100
- Trade-in value: $1,100
- Sales tax rate: 6%
- Sales tax is charged on: The price minus the trade-in
- Sales tax is: Rolled into the loan
- Interest rate (APR): 9.5%
- Loan term: 48 months
- Insurance per year: $500
- Riding gear: $1,400
- Months you ride each year: 8
Find: Monthly payment
Answer
6.
Problem 6.
- Motorcycle price: $11,750
- Down payment: $1,600
- Trade-in value: $1,025
- Sales tax rate: 6%
- Sales tax is charged on: The price minus the trade-in
- Sales tax is: Paid up front
- Interest rate (APR): 8.6%
- Loan term: 60 months
- Insurance per year: $680
- Riding gear: $1,200
- Months you ride each year: 7
Find: Monthly payment
Answer
7.
Problem 7.
- Motorcycle price: $10,750
- Down payment: $1,460
- Trade-in value: $650
- Sales tax rate: 9%
- Sales tax is charged on: The price minus the trade-in
- Sales tax is: Paid up front
- Interest rate (APR): 10%
- Loan term: 24 months
- Insurance per year: $700
- Riding gear: $950
- Months you ride each year: 7
Find: Monthly payment
Answer
8.
Problem 8.
- Motorcycle price: $13,000
- Down payment: $1,700
- Trade-in value: $800
- Sales tax rate: 9%
- Sales tax is charged on: The price minus the trade-in
- Sales tax is: Rolled into the loan
- Interest rate (APR): 9.5%
- Loan term: 24 months
- Insurance per year: $660
- Riding gear: $1,150
- Months you ride each year: 7
Find: Monthly payment
Answer
9.
Problem 9.
- Motorcycle price: $12,000
- Down payment: $1,650
- Trade-in value: $1,200
- Sales tax rate: 7%
- Sales tax is charged on: The full price
- Sales tax is: Paid up front
- Interest rate (APR): 11%
- Loan term: 24 months
- Insurance per year: $600
- Riding gear: $1,250
- Months you ride each year: 10
Find: Monthly payment
Answer
10.
Problem 10.
- Motorcycle price: $13,000
- Down payment: $900
- Trade-in value: $1,100
- Sales tax rate: 7%
- Sales tax is charged on: The full price
- Sales tax is: Paid up front
- Interest rate (APR): 7.5%
- Loan term: 36 months
- Insurance per year: $850
- Riding gear: $1,400
- Months you ride each year: 8
Find: Monthly payment
Answer

Answer key: Motorcycle Loan worksheet

1. Monthly payment: $801.79
1. Find the sales tax. Here it's charged on the price minus your trade-in
  $($19,000.00 - $850.00) \times 6%$ $= $1,089.00$
2. Find how much you borrow: the price, minus your down payment and trade-in, plus the tax
  $$19,000.00 - $1,600.00 - $850.00 + $1,089.00$ $= $17,639.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.085}{12}$ $= 0.00708333$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 24 months
  $\frac{$17,639.00 \times 0.00708333}{1 - {(1 + 0.00708333)}^{−24}}$ $= $801.79$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$801.79 \times 24 - $17,639.00$ $= $1,604.02$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$19,000.00 + $1,089.00 + $1,604.02$ $= $21,693.02$
7. Add your gear to the cash you pay at the start
  $$1,600.00 + $1,200.00$ $= $2,800.00$
8. Add one month of insurance to the loan payment
  $$801.79 + \frac{$675.00}{12}$ $= $858.04$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$801.79 \times 12 + $675.00$ $= $10,296.51$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$10,296.51}{8}$ $= $1,287.06$
11. Add the cash at the start to find what you spend in the first year
  $$2,800.00 + $10,296.51$ $= $13,096.51$
2. Monthly payment: $252.45
1. Find the sales tax. Here it's charged on the price minus your trade-in
  $($13,000.00 - $650.00) \times 9%$ $= $1,111.50$
2. Find how much you borrow: the price, minus your down payment and trade-in, plus the tax
  $$13,000.00 - $1,300.00 - $650.00 + $1,111.50$ $= $12,161.50$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.09}{12}$ $= 0.0075$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 60 months
  $\frac{$12,161.50 \times 0.0075}{1 - {(1 + 0.0075)}^{−60}}$ $= $252.45$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$252.45 \times 60 - $12,161.50$ $= $2,985.66$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$13,000.00 + $1,111.50 + $2,985.66$ $= $17,097.16$
7. Add your gear to the cash you pay at the start
  $$1,300.00 + $1,000.00$ $= $2,300.00$
8. Add one month of insurance to the loan payment
  $$252.45 + \frac{$800.00}{12}$ $= $319.12$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$252.45 \times 12 + $800.00$ $= $3,829.43$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$3,829.43}{11}$ $= $348.13$
11. Add the cash at the start to find what you spend in the first year
  $$2,300.00 + $3,829.43$ $= $6,129.43$
3. Monthly payment: $366.43
1. Find the sales tax. Here it's charged on the full price of the motorcycle
  $$17,000.00 \times 8%$ $= $1,360.00$
2. Find how much you borrow: the price, minus your down payment and trade-in. You pay the tax up front
  $$17,000.00 - $1,200.00 - $1,075.00$ $= $14,725.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.09}{12}$ $= 0.0075$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 48 months
  $\frac{$14,725.00 \times 0.0075}{1 - {(1 + 0.0075)}^{−48}}$ $= $366.43$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$366.43 \times 48 - $14,725.00$ $= $2,863.75$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$17,000.00 + $1,360.00 + $2,863.75$ $= $21,223.75$
7. Add your gear to the cash you pay at the start
  $$2,560.00 + $1,000.00$ $= $3,560.00$
8. Add one month of insurance to the loan payment
  $$366.43 + \frac{$500.00}{12}$ $= $408.10$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$366.43 \times 12 + $500.00$ $= $4,897.19$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$4,897.19}{7}$ $= $699.60$
11. Add the cash at the start to find what you spend in the first year
  $$3,560.00 + $4,897.19$ $= $8,457.19$
4. Monthly payment: $648.07
1. Find the sales tax. Here it's charged on the price minus your trade-in
  $($21,500.00 - $1,050.00) \times 10%$ $= $2,045.00$
2. Find how much you borrow: the price, minus your down payment and trade-in, plus the tax
  $$21,500.00 - $1,350.00 - $1,050.00 + $2,045.00$ $= $21,145.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.065}{12}$ $= 0.00541667$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 36 months
  $\frac{$21,145.00 \times 0.00541667}{1 - {(1 + 0.00541667)}^{−36}}$ $= $648.07$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$648.07 \times 36 - $21,145.00$ $= $2,185.63$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$21,500.00 + $2,045.00 + $2,185.63$ $= $25,730.63$
7. Add your gear to the cash you pay at the start
  $$1,350.00 + $1,200.00$ $= $2,550.00$
8. Add one month of insurance to the loan payment
  $$648.07 + \frac{$750.00}{12}$ $= $710.57$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$648.07 \times 12 + $750.00$ $= $8,526.88$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$8,526.88}{6}$ $= $1,421.15$
11. Add the cash at the start to find what you spend in the first year
  $$2,550.00 + $8,526.88$ $= $11,076.88$
5. Monthly payment: $182.75
1. Find the sales tax. Here it's charged on the price minus your trade-in
  $($9,000.00 - $1,100.00) \times 6%$ $= $474.00$
2. Find how much you borrow: the price, minus your down payment and trade-in, plus the tax
  $$9,000.00 - $1,100.00 - $1,100.00 + $474.00$ $= $7,274.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.095}{12}$ $= 0.00791667$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 48 months
  $\frac{$7,274.00 \times 0.00791667}{1 - {(1 + 0.00791667)}^{−48}}$ $= $182.75$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$182.75 \times 48 - $7,274.00$ $= $1,497.79$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$9,000.00 + $474.00 + $1,497.79$ $= $10,971.79$
7. Add your gear to the cash you pay at the start
  $$1,100.00 + $1,400.00$ $= $2,500.00$
8. Add one month of insurance to the loan payment
  $$182.75 + \frac{$500.00}{12}$ $= $224.41$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$182.75 \times 12 + $500.00$ $= $2,692.95$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$2,692.95}{8}$ $= $336.62$
11. Add the cash at the start to find what you spend in the first year
  $$2,500.00 + $2,692.95$ $= $5,192.95$
6. Monthly payment: $187.65
1. Find the sales tax. Here it's charged on the price minus your trade-in
  $($11,750.00 - $1,025.00) \times 6%$ $= $643.50$
2. Find how much you borrow: the price, minus your down payment and trade-in. You pay the tax up front
  $$11,750.00 - $1,600.00 - $1,025.00$ $= $9,125.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.086}{12}$ $= 0.00716667$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 60 months
  $\frac{$9,125.00 \times 0.00716667}{1 - {(1 + 0.00716667)}^{−60}}$ $= $187.65$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$187.65 \times 60 - $9,125.00$ $= $2,134.21$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$11,750.00 + $643.50 + $2,134.21$ $= $14,527.71$
7. Add your gear to the cash you pay at the start
  $$2,243.50 + $1,200.00$ $= $3,443.50$
8. Add one month of insurance to the loan payment
  $$187.65 + \frac{$680.00}{12}$ $= $244.32$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$187.65 \times 12 + $680.00$ $= $2,931.84$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$2,931.84}{7}$ $= $418.83$
11. Add the cash at the start to find what you spend in the first year
  $$3,443.50 + $2,931.84$ $= $6,375.34$
7. Monthly payment: $398.69
1. Find the sales tax. Here it's charged on the price minus your trade-in
  $($10,750.00 - $650.00) \times 9%$ $= $909.00$
2. Find how much you borrow: the price, minus your down payment and trade-in. You pay the tax up front
  $$10,750.00 - $1,460.00 - $650.00$ $= $8,640.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.1}{12}$ $= 0.00833333$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 24 months
  $\frac{$8,640.00 \times 0.00833333}{1 - {(1 + 0.00833333)}^{−24}}$ $= $398.69$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$398.69 \times 24 - $8,640.00$ $= $928.61$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$10,750.00 + $909.00 + $928.61$ $= $12,587.61$
7. Add your gear to the cash you pay at the start
  $$2,369.00 + $950.00$ $= $3,319.00$
8. Add one month of insurance to the loan payment
  $$398.69 + \frac{$700.00}{12}$ $= $457.03$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$398.69 \times 12 + $700.00$ $= $5,484.31$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$5,484.31}{7}$ $= $783.47$
11. Add the cash at the start to find what you spend in the first year
  $$3,319.00 + $5,484.31$ $= $8,803.31$
8. Monthly payment: $532.52
1. Find the sales tax. Here it's charged on the price minus your trade-in
  $($13,000.00 - $800.00) \times 9%$ $= $1,098.00$
2. Find how much you borrow: the price, minus your down payment and trade-in, plus the tax
  $$13,000.00 - $1,700.00 - $800.00 + $1,098.00$ $= $11,598.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.095}{12}$ $= 0.00791667$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 24 months
  $\frac{$11,598.00 \times 0.00791667}{1 - {(1 + 0.00791667)}^{−24}}$ $= $532.52$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$532.52 \times 24 - $11,598.00$ $= $1,182.39$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$13,000.00 + $1,098.00 + $1,182.39$ $= $15,280.39$
7. Add your gear to the cash you pay at the start
  $$1,700.00 + $1,150.00$ $= $2,850.00$
8. Add one month of insurance to the loan payment
  $$532.52 + \frac{$660.00}{12}$ $= $587.52$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$532.52 \times 12 + $660.00$ $= $7,050.20$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$7,050.20}{7}$ $= $1,007.17$
11. Add the cash at the start to find what you spend in the first year
  $$2,850.00 + $7,050.20$ $= $9,900.20$
9. Monthly payment: $426.46
1. Find the sales tax. Here it's charged on the full price of the motorcycle
  $$12,000.00 \times 7%$ $= $840.00$
2. Find how much you borrow: the price, minus your down payment and trade-in. You pay the tax up front
  $$12,000.00 - $1,650.00 - $1,200.00$ $= $9,150.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.11}{12}$ $= 0.00916667$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 24 months
  $\frac{$9,150.00 \times 0.00916667}{1 - {(1 + 0.00916667)}^{−24}}$ $= $426.46$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$426.46 \times 24 - $9,150.00$ $= $1,085.08$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$12,000.00 + $840.00 + $1,085.08$ $= $13,925.08$
7. Add your gear to the cash you pay at the start
  $$2,490.00 + $1,250.00$ $= $3,740.00$
8. Add one month of insurance to the loan payment
  $$426.46 + \frac{$600.00}{12}$ $= $476.46$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$426.46 \times 12 + $600.00$ $= $5,717.54$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$5,717.54}{10}$ $= $571.75$
11. Add the cash at the start to find what you spend in the first year
  $$3,740.00 + $5,717.54$ $= $9,457.54$
10. Monthly payment: $342.17
1. Find the sales tax. Here it's charged on the full price of the motorcycle
  $$13,000.00 \times 7%$ $= $910.00$
2. Find how much you borrow: the price, minus your down payment and trade-in. You pay the tax up front
  $$13,000.00 - $900.00 - $1,100.00$ $= $11,000.00$
3. Divide the yearly rate by 12 to get the monthly rate, because interest is charged every month
  $i$ $= \frac{0.075}{12}$ $= 0.00625$
4. Find the monthly payment. A standard formula gives the one amount that pays off the loan, with interest, in 36 months
  $\frac{$11,000.00 \times 0.00625}{1 - {(1 + 0.00625)}^{−36}}$ $= $342.17$
5. Find the total interest: all your payments added up, minus what you borrowed
  $$342.17 \times 36 - $11,000.00$ $= $1,318.06$
6. Find the total cost of the motorcycle: the price, the tax and the interest
  $$13,000.00 + $910.00 + $1,318.06$ $= $15,228.06$
7. Add your gear to the cash you pay at the start
  $$1,810.00 + $1,400.00$ $= $3,210.00$
8. Add one month of insurance to the loan payment
  $$342.17 + \frac{$850.00}{12}$ $= $413.00$
9. Add a year of loan payments and insurance. You pay both even in months the bike stays parked
  $$342.17 \times 12 + $850.00$ $= $4,956.02$
10. Divide by the months you ride to see what each riding month really costs
  $\frac{$4,956.02}{8}$ $= $619.50$
11. Add the cash at the start to find what you spend in the first year
  $$3,210.00 + $4,956.02$ $= $8,166.02$