APR worksheet

1. APR: 7.781%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=10\times 12$$=120$

2. You borrow the fees too, so the payment is based on the loan plus the fees

   $\text{balance}$$=\mathrm{\$20,000.00}+\mathrm{\$700.00}$$=\mathrm{\$20,700.00}$

3. Find the monthly payment at 7% interest. A standard formula gives the one amount that pays off the loan in 120 equal payments

   $\frac{\mathrm{\$20,700.00}\times 0.00583333}{1-{\left(1+0.00583333\right)}^{\mathrm{-120}}}$$=\mathrm{\$240.34}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$20,000.00}$$=\mathrm{\$240.34}\times \frac{1-{\left(1+j\right)}^{\mathrm{-120}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00648397$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00648397\times 12\times 100$$=\mathrm{7.7808\%}$

2. APR: 8.542%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=5\times 12$$=60$

2. The fees come out at the start, so the cash you really get is the loan minus the fees

   $\text{received}$$=\mathrm{\$14,500.00}-\mathrm{\$850.00}$$=\mathrm{\$13,650.00}$

3. Find the monthly payment at 6% interest. A standard formula gives the one amount that pays off the loan in 60 equal payments

   $\frac{\mathrm{\$14,500.00}\times 0.005}{1-{\left(1+0.005\right)}^{\mathrm{-60}}}$$=\mathrm{\$280.33}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$13,650.00}$$=\mathrm{\$280.33}\times \frac{1-{\left(1+j\right)}^{\mathrm{-60}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00711815$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00711815\times 12\times 100$$=\mathrm{8.5418\%}$

3. APR: 10.005%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=7\times 12$$=84$

2. You borrow the fees too, so the payment is based on the loan plus the fees

   $\text{balance}$$=\mathrm{\$20,000.00}+\mathrm{\$640.00}$$=\mathrm{\$20,640.00}$

3. Find the monthly payment at 9% interest. A standard formula gives the one amount that pays off the loan in 84 equal payments

   $\frac{\mathrm{\$20,640.00}\times 0.0075}{1-{\left(1+0.0075\right)}^{\mathrm{-84}}}$$=\mathrm{\$332.08}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$20,000.00}$$=\mathrm{\$332.08}\times \frac{1-{\left(1+j\right)}^{\mathrm{-84}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00833776$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00833776\times 12\times 100$$=\mathrm{10.0053\%}$

4. APR: 7.928%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=10\times 12$$=120$

2. The fees come out at the start, so the cash you really get is the loan minus the fees

   $\text{received}$$=\mathrm{\$20,000.00}-\mathrm{\$800.00}$$=\mathrm{\$19,200.00}$

3. Find the monthly payment at 7% interest. A standard formula gives the one amount that pays off the loan in 120 equal payments

   $\frac{\mathrm{\$20,000.00}\times 0.00583333}{1-{\left(1+0.00583333\right)}^{\mathrm{-120}}}$$=\mathrm{\$232.22}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$19,200.00}$$=\mathrm{\$232.22}\times \frac{1-{\left(1+j\right)}^{\mathrm{-120}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00660649$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00660649\times 12\times 100$$=\mathrm{7.9278\%}$

5. APR: 8.025%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=4\times 12$$=48$

2. You borrow the fees too, so the payment is based on the loan plus the fees

   $\text{balance}$$=\mathrm{\$27,500.00}+\mathrm{\$1,100.00}$$=\mathrm{\$28,600.00}$

3. Find the monthly payment at 6% interest. A standard formula gives the one amount that pays off the loan in 48 equal payments

   $\frac{\mathrm{\$28,600.00}\times 0.005}{1-{\left(1+0.005\right)}^{\mathrm{-48}}}$$=\mathrm{\$671.67}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$27,500.00}$$=\mathrm{\$671.67}\times \frac{1-{\left(1+j\right)}^{\mathrm{-48}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00668709$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00668709\times 12\times 100$$=\mathrm{8.0245\%}$

6. APR: 7.032%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=4\times 12$$=48$

2. The fees come out at the start, so the cash you really get is the loan minus the fees

   $\text{received}$$=\mathrm{\$22,500.00}-\mathrm{\$875.00}$$=\mathrm{\$21,625.00}$

3. Find the monthly payment at 5% interest. A standard formula gives the one amount that pays off the loan in 48 equal payments

   $\frac{\mathrm{\$22,500.00}\times 0.00416667}{1-{\left(1+0.00416667\right)}^{\mathrm{-48}}}$$=\mathrm{\$518.16}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$21,625.00}$$=\mathrm{\$518.16}\times \frac{1-{\left(1+j\right)}^{\mathrm{-48}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00586004$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00586004\times 12\times 100$$=\mathrm{7.032\%}$

7. APR: 8.226%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=5\times 12$$=60$

2. You borrow the fees too, so the payment is based on the loan plus the fees

   $\text{balance}$$=\mathrm{\$19,000.00}+\mathrm{\$560.00}$$=\mathrm{\$19,560.00}$

3. Find the monthly payment at 7% interest. A standard formula gives the one amount that pays off the loan in 60 equal payments

   $\frac{\mathrm{\$19,560.00}\times 0.00583333}{1-{\left(1+0.00583333\right)}^{\mathrm{-60}}}$$=\mathrm{\$387.31}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$19,000.00}$$=\mathrm{\$387.31}\times \frac{1-{\left(1+j\right)}^{\mathrm{-60}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00685515$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00685515\times 12\times 100$$=\mathrm{8.2262\%}$

8. APR: 8.048%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=10\times 12$$=120$

2. The fees come out at the start, so the cash you really get is the loan minus the fees

   $\text{received}$$=\mathrm{\$20,000.00}-\mathrm{\$900.00}$$=\mathrm{\$19,100.00}$

3. Find the monthly payment at 7% interest. A standard formula gives the one amount that pays off the loan in 120 equal payments

   $\frac{\mathrm{\$20,000.00}\times 0.00583333}{1-{\left(1+0.00583333\right)}^{\mathrm{-120}}}$$=\mathrm{\$232.22}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$19,100.00}$$=\mathrm{\$232.22}\times \frac{1-{\left(1+j\right)}^{\mathrm{-120}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00670638$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00670638\times 12\times 100$$=\mathrm{8.0477\%}$

9. APR: 6.649%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=7\times 12$$=84$

2. The fees come out at the start, so the cash you really get is the loan minus the fees

   $\text{received}$$=\mathrm{\$25,000.00}-\mathrm{\$525.00}$$=\mathrm{\$24,475.00}$

3. Find the monthly payment at 6% interest. A standard formula gives the one amount that pays off the loan in 84 equal payments

   $\frac{\mathrm{\$25,000.00}\times 0.005}{1-{\left(1+0.005\right)}^{\mathrm{-84}}}$$=\mathrm{\$365.21}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$24,475.00}$$=\mathrm{\$365.21}\times \frac{1-{\left(1+j\right)}^{\mathrm{-84}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00554124$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00554124\times 12\times 100$$=\mathrm{6.6495\%}$

10. APR: 10.558%

1. Count the monthly payments (n): 12 for every year of the loan

   $n$$=4\times 12$$=48$

2. You borrow the fees too, so the payment is based on the loan plus the fees

   $\text{balance}$$=\mathrm{\$20,000.00}+\mathrm{\$600.00}$$=\mathrm{\$20,600.00}$

3. Find the monthly payment at 9% interest. A standard formula gives the one amount that pays off the loan in 48 equal payments

   $\frac{\mathrm{\$20,600.00}\times 0.0075}{1-{\left(1+0.0075\right)}^{\mathrm{-48}}}$$=\mathrm{\$512.63}$

4. Now find the monthly rate j that makes those payments worth exactly the cash you got

   $\mathrm{\$20,000.00}$$=\mathrm{\$512.63}\times \frac{1-{\left(1+j\right)}^{\mathrm{-48}}}{j}$

5. There is no direct formula, so the calculator tries rates until both sides match

   $j$$=0.00879867$

6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

   $\text{APR}$$=0.00879867\times 12\times 100$$=\mathrm{10.5584\%}$