Printable worksheet

← Back to the Personal Loan Calculator

In the print window, choose “Save as PDF” as the printer (or print it on paper). Seed 1 rebuilds this exact sheet.

Personal Loan worksheet

Grade 12 to college · CCSS HSA.SSE.B.4

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

1.
Problem 1.
- Loan amount: $15,000
- Interest rate: 10%
- Loan term: 5 years
- Origination fee: 5% of loan
- How the fee is paid: Added to the loan balance
Find: Monthly payment
Answer
2.
Problem 2.
- Loan amount: $17,500
- Interest rate: 11.5%
- Loan term: 3 years
- Origination fee: 0% of loan
- How the fee is paid: Taken out of the money you receive
Find: Monthly payment
Answer
3.
Problem 3.
- Loan amount: $13,500
- Interest rate: 10%
- Loan term: 2 years
- Origination fee: 3% of loan
- How the fee is paid: Taken out of the money you receive
Find: Monthly payment
Answer
4.
Problem 4.
- Loan amount: $14,000
- Interest rate: 14%
- Loan term: 5 years
- Origination fee: 0% of loan
- How the fee is paid: Added to the loan balance
Find: Monthly payment
Answer
5.
Problem 5.
- Loan amount: $19,500
- Interest rate: 18%
- Loan term: 2 years
- Origination fee: 1% of loan
- How the fee is paid: Added to the loan balance
Find: Monthly payment
Answer
6.
Problem 6.
- Loan amount: $13,000
- Interest rate: 8%
- Loan term: 3 years
- Origination fee: 0% of loan
- How the fee is paid: Taken out of the money you receive
Find: Monthly payment
Answer
7.
Problem 7.
- Loan amount: $18,000
- Interest rate: 11.5%
- Loan term: 3 years
- Origination fee: 5% of loan
- How the fee is paid: Added to the loan balance
Find: Monthly payment
Answer
8.
Problem 8.
- Loan amount: $20,000
- Interest rate: 24%
- Loan term: 2 years
- Origination fee: 0% of loan
- How the fee is paid: Added to the loan balance
Find: Monthly payment
Answer
9.
Problem 9.
- Loan amount: $16,000
- Interest rate: 18%
- Loan term: 2 years
- Origination fee: 5% of loan
- How the fee is paid: Added to the loan balance
Find: Monthly payment
Answer
10.
Problem 10.
- Loan amount: $14,000
- Interest rate: 8%
- Loan term: 4 years
- Origination fee: 1% of loan
- How the fee is paid: Added to the loan balance
Find: Monthly payment
Answer

Answer key: Personal Loan worksheet

1. Monthly payment: $334.64
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 5 \times 12$ $= 60$
2. Work out the fee in dollars: 5% of the loan amount
  $$15,000.00 \times 5%$ $= $750.00$
3. The fee is added to what you owe, so you repay more than the cash you get
  $$15,000.00 + $750.00$ $= $15,750.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.1}{12}$ $= 0.00833333$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$15,750.00 \times 0.00833333}{1 - {(1 + 0.00833333)}^{−60}}$ $= $334.64$
6. Find the total interest: all your payments, minus what you owe at the start
  $$334.64 \times 60 - $15,750.00$ $= $4,328.46$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$20,078.46 - $15,000.00$ $= $5,078.46$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.01010702 \times 12$ $= 12.1284%$
2. Monthly payment: $577.08
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 3 \times 12$ $= 36$
2. Work out the fee in dollars: 0% of the loan amount
  $$17,500.00 \times 0%$ $= $0.00$
3. The lender keeps the fee, so subtract it to find the cash you actually get. You still repay the full loan amount
  $$17,500.00 - $0.00$ $= $17,500.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.115}{12}$ $= 0.00958333$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$17,500.00 \times 0.00958333}{1 - {(1 + 0.00958333)}^{−36}}$ $= $577.08$
6. Find the total interest: all your payments, minus what you owe at the start
  $$577.08 \times 36 - $17,500.00$ $= $3,274.88$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$20,774.88 - $17,500.00$ $= $3,274.88$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.00958333 \times 12$ $= 11.5%$
3. Monthly payment: $622.96
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 2 \times 12$ $= 24$
2. Work out the fee in dollars: 3% of the loan amount
  $$13,500.00 \times 3%$ $= $405.00$
3. The lender keeps the fee, so subtract it to find the cash you actually get. You still repay the full loan amount
  $$13,500.00 - $405.00$ $= $13,095.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.1}{12}$ $= 0.00833333$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$13,500.00 \times 0.00833333}{1 - {(1 + 0.00833333)}^{−24}}$ $= $622.96$
6. Find the total interest: all your payments, minus what you owe at the start
  $$622.96 \times 24 - $13,500.00$ $= $1,450.96$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$14,950.96 - $13,095.00$ $= $1,855.96$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.01088702 \times 12$ $= 13.0644%$
4. Monthly payment: $325.76
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 5 \times 12$ $= 60$
2. Work out the fee in dollars: 0% of the loan amount
  $$14,000.00 \times 0%$ $= $0.00$
3. The fee is added to what you owe, so you repay more than the cash you get
  $$14,000.00 + $0.00$ $= $14,000.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.14}{12}$ $= 0.01166667$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$14,000.00 \times 0.01166667}{1 - {(1 + 0.01166667)}^{−60}}$ $= $325.76$
6. Find the total interest: all your payments, minus what you owe at the start
  $$325.76 \times 60 - $14,000.00$ $= $5,545.33$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$19,545.33 - $14,000.00$ $= $5,545.33$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.01166667 \times 12$ $= 14%$
5. Monthly payment: $983.26
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 2 \times 12$ $= 24$
2. Work out the fee in dollars: 1% of the loan amount
  $$19,500.00 \times 1%$ $= $195.00$
3. The fee is added to what you owe, so you repay more than the cash you get
  $$19,500.00 + $195.00$ $= $19,695.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.18}{12}$ $= 0.015$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$19,695.00 \times 0.015}{1 - {(1 + 0.015)}^{−24}}$ $= $983.26$
6. Find the total interest: all your payments, minus what you owe at the start
  $$983.26 \times 24 - $19,695.00$ $= $3,903.12$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$23,598.12 - $19,500.00$ $= $4,098.12$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.01585859 \times 12$ $= 19.0303%$
6. Monthly payment: $407.37
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 3 \times 12$ $= 36$
2. Work out the fee in dollars: 0% of the loan amount
  $$13,000.00 \times 0%$ $= $0.00$
3. The lender keeps the fee, so subtract it to find the cash you actually get. You still repay the full loan amount
  $$13,000.00 - $0.00$ $= $13,000.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.08}{12}$ $= 0.00666667$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$13,000.00 \times 0.00666667}{1 - {(1 + 0.00666667)}^{−36}}$ $= $407.37$
6. Find the total interest: all your payments, minus what you owe at the start
  $$407.37 \times 36 - $13,000.00$ $= $1,665.42$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$14,665.42 - $13,000.00$ $= $1,665.42$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.00666667 \times 12$ $= 8%$
7. Monthly payment: $623.25
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 3 \times 12$ $= 36$
2. Work out the fee in dollars: 5% of the loan amount
  $$18,000.00 \times 5%$ $= $900.00$
3. The fee is added to what you owe, so you repay more than the cash you get
  $$18,000.00 + $900.00$ $= $18,900.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.115}{12}$ $= 0.00958333$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$18,900.00 \times 0.00958333}{1 - {(1 + 0.00958333)}^{−36}}$ $= $623.25$
6. Find the total interest: all your payments, minus what you owe at the start
  $$623.25 \times 36 - $18,900.00$ $= $3,536.87$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$22,436.87 - $18,000.00$ $= $4,436.87$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.01243102 \times 12$ $= 14.9172%$
8. Monthly payment: $1,057.42
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 2 \times 12$ $= 24$
2. Work out the fee in dollars: 0% of the loan amount
  $$20,000.00 \times 0%$ $= $0.00$
3. The fee is added to what you owe, so you repay more than the cash you get
  $$20,000.00 + $0.00$ $= $20,000.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.24}{12}$ $= 0.02$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$20,000.00 \times 0.02}{1 - {(1 + 0.02)}^{−24}}$ $= $1,057.42$
6. Find the total interest: all your payments, minus what you owe at the start
  $$1,057.42 \times 24 - $20,000.00$ $= $5,378.13$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$25,378.13 - $20,000.00$ $= $5,378.13$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.02 \times 12$ $= 24%$
9. Monthly payment: $838.72
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 2 \times 12$ $= 24$
2. Work out the fee in dollars: 5% of the loan amount
  $$16,000.00 \times 5%$ $= $800.00$
3. The fee is added to what you owe, so you repay more than the cash you get
  $$16,000.00 + $800.00$ $= $16,800.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.18}{12}$ $= 0.015$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$16,800.00 \times 0.015}{1 - {(1 + 0.015)}^{−24}}$ $= $838.72$
6. Find the total interest: all your payments, minus what you owe at the start
  $$838.72 \times 24 - $16,800.00$ $= $3,329.40$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$20,129.40 - $16,000.00$ $= $4,129.40$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.01924554 \times 12$ $= 23.0946%$
10. Monthly payment: $345.20
1. Count your monthly payments (n): 12 for each year of the loan
  $n$ $= 4 \times 12$ $= 48$
2. Work out the fee in dollars: 1% of the loan amount
  $$14,000.00 \times 1%$ $= $140.00$
3. The fee is added to what you owe, so you repay more than the cash you get
  $$14,000.00 + $140.00$ $= $14,140.00$
4. Turn the yearly rate into a monthly rate (i) by dividing by 12, because interest is charged every month
  $i$ $= \frac{0.08}{12}$ $= 0.00666667$
5. Find the monthly payment. A standard formula gives the one amount that pays off what you owe, with interest, in n months
  $\frac{$14,140.00 \times 0.00666667}{1 - {(1 + 0.00666667)}^{−48}}$ $= $345.20$
6. Find the total interest: all your payments, minus what you owe at the start
  $$345.20 \times 48 - $14,140.00$ $= $2,429.54$
7. Find the full cost of borrowing: everything you pay back, minus the cash you got. This is the interest plus the fee
  $$16,569.54 - $14,000.00$ $= $2,569.54$
8. Find the true APR: the yearly rate at which your payments are worth exactly the cash you got. The calculator tries rates until one fits
  $true APR$ $= 0.00709877 \times 12$ $= 8.5185%$