Credit Card Interest worksheet

1. Months to pay off with minimums: 133

1. Interest is charged monthly, so the monthly rate is the APR as a decimal divided by 12

   $i$$=\frac{0.26}{12}$$=0.02166667$

2. The first month's interest is the balance times the monthly rate

   $\mathrm{\$3,500.00}\times 0.02166667$$=\mathrm{\$75.83}$

3. The percent part of the first minimum is 2% of the balance plus the month's interest

   $\mathrm{\$3,500.00}\times \mathrm{2\%}+\mathrm{\$75.83}$$=\mathrm{\$145.83}$

4. Repeat every month: add interest, then pay the new minimum. The minimum shrinks as the balance does, which is why it takes so long

   $\text{months until the balance is zero}$$=133$

5. Find the total interest: everything you paid minus the balance you started with

   $\mathrm{\$6,976.49}-\mathrm{\$3,500.00}$$=\mathrm{\$3,476.49}$

6. Put the number of months in years and months

   $\text{11 years 1 month}$

2. Interest this billing cycle: $54.49

1. Cards charge interest daily, so the daily periodic rate is the APR as a decimal divided by 365

   $\text{DPR}$$=\frac{0.225}{365}$$=0.00061644$

2. Interest for one day is the balance times the daily rate

   $\mathrm{\$3,400.00}\times 0.00061644$$=\mathrm{\$2.10}$

3. Multiply by the 26 days in the cycle

   $\mathrm{\$3,400.00}\times 0.00061644\times 26$$=\mathrm{\$54.49}$

4. As a cross-check, a year of interest at this balance is the balance times the APR

   $\mathrm{\$3,400.00}\times \mathrm{22.5\%}$$=\mathrm{\$765.00}$

3. Months to pay off with minimums: 206

1. Interest is charged monthly, so the monthly rate is the APR as a decimal divided by 12

   $i$$=\frac{0.3}{12}$$=0.025$

2. The first month's interest is the balance times the monthly rate

   $\mathrm{\$3,250.00}\times 0.025$$=\mathrm{\$81.25}$

3. The percent part of the first minimum is 1% of the balance plus the month's interest

   $\mathrm{\$3,250.00}\times \mathrm{1\%}+\mathrm{\$81.25}$$=\mathrm{\$113.75}$

4. Repeat every month: add interest, then pay the new minimum. The minimum shrinks as the balance does, which is why it takes so long

   $\text{months until the balance is zero}$$=206$

5. Find the total interest: everything you paid minus the balance you started with

   $\mathrm{\$10,192.65}-\mathrm{\$3,250.00}$$=\mathrm{\$6,942.65}$

6. Put the number of months in years and months

   $\text{17 years 2 months}$

4. Interest this billing cycle: $61.64

1. Cards charge interest daily, so the daily periodic rate is the APR as a decimal divided by 365

   $\text{DPR}$$=\frac{0.25}{365}$$=0.00068493$

2. Interest for one day is the balance times the daily rate

   $\mathrm{\$3,750.00}\times 0.00068493$$=\mathrm{\$2.57}$

3. Multiply by the 24 days in the cycle

   $\mathrm{\$3,750.00}\times 0.00068493\times 24$$=\mathrm{\$61.64}$

4. As a cross-check, a year of interest at this balance is the balance times the APR

   $\mathrm{\$3,750.00}\times \mathrm{25\%}$$=\mathrm{\$937.50}$

5. Months to pay off with minimums: 201

1. Interest is charged monthly, so the monthly rate is the APR as a decimal divided by 12

   $i$$=\frac{0.24}{12}$$=0.02$

2. The first month's interest is the balance times the monthly rate

   $\mathrm{\$3,000.00}\times 0.02$$=\mathrm{\$60.00}$

3. The percent part of the first minimum is 1% of the balance plus the month's interest

   $\mathrm{\$3,000.00}\times \mathrm{1\%}+\mathrm{\$60.00}$$=\mathrm{\$90.00}$

4. Repeat every month: add interest, then pay the new minimum. The minimum shrinks as the balance does, which is why it takes so long

   $\text{months until the balance is zero}$$=201$

5. Find the total interest: everything you paid minus the balance you started with

   $\mathrm{\$8,065.05}-\mathrm{\$3,000.00}$$=\mathrm{\$5,065.05}$

6. Put the number of months in years and months

   $\text{16 years 9 months}$

6. Interest this billing cycle: $41.05

1. Cards charge interest daily, so the daily periodic rate is the APR as a decimal divided by 365

   $\text{DPR}$$=\frac{0.225}{365}$$=0.00061644$

2. Interest for one day is the balance times the daily rate

   $\mathrm{\$3,700.00}\times 0.00061644$$=\mathrm{\$2.28}$

3. Multiply by the 18 days in the cycle

   $\mathrm{\$3,700.00}\times 0.00061644\times 18$$=\mathrm{\$41.05}$

4. As a cross-check, a year of interest at this balance is the balance times the APR

   $\mathrm{\$3,700.00}\times \mathrm{22.5\%}$$=\mathrm{\$832.50}$

7. Interest this billing cycle: $80.16

1. Cards charge interest daily, so the daily periodic rate is the APR as a decimal divided by 365

   $\text{DPR}$$=\frac{0.35}{365}$$=0.0009589$

2. Interest for one day is the balance times the daily rate

   $\mathrm{\$3,800.00}\times 0.0009589$$=\mathrm{\$3.64}$

3. Multiply by the 22 days in the cycle

   $\mathrm{\$3,800.00}\times 0.0009589\times 22$$=\mathrm{\$80.16}$

4. As a cross-check, a year of interest at this balance is the balance times the APR

   $\mathrm{\$3,800.00}\times \mathrm{35\%}$$=\mathrm{\$1,330.00}$

8. Interest this billing cycle: $70.52

1. Cards charge interest daily, so the daily periodic rate is the APR as a decimal divided by 365

   $\text{DPR}$$=\frac{0.26}{365}$$=0.00071233$

2. Interest for one day is the balance times the daily rate

   $\mathrm{\$4,500.00}\times 0.00071233$$=\mathrm{\$3.21}$

3. Multiply by the 22 days in the cycle

   $\mathrm{\$4,500.00}\times 0.00071233\times 22$$=\mathrm{\$70.52}$

4. As a cross-check, a year of interest at this balance is the balance times the APR

   $\mathrm{\$4,500.00}\times \mathrm{26\%}$$=\mathrm{\$1,170.00}$

9. Months to pay off with minimums: 102

1. Interest is charged monthly, so the monthly rate is the APR as a decimal divided by 12

   $i$$=\frac{0.24}{12}$$=0.02$

2. The first month's interest is the balance times the monthly rate

   $\mathrm{\$2,400.00}\times 0.02$$=\mathrm{\$48.00}$

3. The percent part of the first minimum is 2% of the balance plus the month's interest

   $\mathrm{\$2,400.00}\times \mathrm{2\%}+\mathrm{\$48.00}$$=\mathrm{\$96.00}$

4. Repeat every month: add interest, then pay the new minimum. The minimum shrinks as the balance does, which is why it takes so long

   $\text{months until the balance is zero}$$=102$

5. Find the total interest: everything you paid minus the balance you started with

   $\mathrm{\$4,425.07}-\mathrm{\$2,400.00}$$=\mathrm{\$2,025.07}$

6. Put the number of months in years and months

   $\text{8 years 6 months}$

10. Months to pay off with minimums: 135

1. Interest is charged monthly, so the monthly rate is the APR as a decimal divided by 12

   $i$$=\frac{0.24}{12}$$=0.02$

2. The first month's interest is the balance times the monthly rate

   $\mathrm{\$3,700.00}\times 0.02$$=\mathrm{\$74.00}$

3. The percent part of the first minimum is 2% of the balance plus the month's interest

   $\mathrm{\$3,700.00}\times \mathrm{2\%}+\mathrm{\$74.00}$$=\mathrm{\$148.00}$

4. Repeat every month: add interest, then pay the new minimum. The minimum shrinks as the balance does, which is why it takes so long

   $\text{months until the balance is zero}$$=135$

5. Find the total interest: everything you paid minus the balance you started with

   $\mathrm{\$7,100.06}-\mathrm{\$3,700.00}$$=\mathrm{\$3,400.06}$

6. Put the number of months in years and months

   $\text{11 years 3 months}$