Question

You owe $2000 on a credit card. The card charges 1.5% monthly interest on your balance, and requires a minimum monthly payment of 2.5% of your balance. All transactions (payments and interest charges) are recorded at the end of the month. You make only the minimum payment every month and incur no additional debt.

A) Complete the table for a twelve month period.

B) What is your unpaid balance after one year had passed?

C) At that time, how much of your debt have you paid off?

D) How much money in interest charges have you paid your creditors?

Answer 1

Over a twelve month period, starting with a $2000 balance, the unpaid balance after one year is $1790.77. During that time, $209.23 of the debt was paid off, and a total of $331.56 was paid in interest charges to creditors.

A) Complete the table for a twelve month period:

- Month 0: Balance = $2000.00, Interest = $30.00, Minimum Payment = $50.00

- Month 1: Balance = $1980.00, Interest = $29.70, Minimum Payment = $49.50

- Month 2: Balance = $1960.20, Interest = $29.40, Minimum Payment = $49.00

- Month 3: Balance = $1940.60, Interest = $29.11, Minimum Payment = $48.51

- Month 4: Balance = $1921.19, Interest = $28.82, Minimum Payment = $48.03

- Month 5: Balance = $1901.98, Interest = $28.53, Minimum Payment = $47.55

- Month 6: Balance = $1882.97, Interest = $28.24, Minimum Payment = $47.07

- Month 7: Balance = $1864.15, Interest = $27.86, Minimum Payment = $46.60

- Month 8: Balance = $1845.52, Interest = $27.68, Minimum Payment = $46.14

- Month 9: Balance = $1827.08, Interest = $27.41, Minimum Payment = $45.68

- Month 10: Balance = $1808.83, Interest = $27.13, Minimum Payment = $45.22

- Month 11: Balance = $1790.77, Interest = $26.86, Minimum Payment = $44.77

B) The unpaid balance after one year has passed is $1790.77.

C) At that time, you have paid off $2000 - $1790.77 = $209.23 of your debt.

D) Over the year, you have paid a total of $331.56 in interest charges to your creditors ($30 + $29.70 + $29.40 + $29.11 + $28.82 + $28.53 + $28.24 + $27.86 + $27.68 + $27.41 + $27.13 + $26.86).

Answer 2

A) see below

B) $1476.00

C) $524.00

D) $314.41

Explanation:

This is most conveniently done using a spreadsheet program, such as Microsoft Excel or Google Sheets. The latter is one of many free or low-cost spreadsheet programs available for a number of platforms, including phones, tablets, and personal computers.

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As the problem statement tells you, the amount of interest paid is 0.015 times the balance.

As the problem statement tells you, the minimum payment is 0.025 times the balance.

Of course, the new balance is the difference between the previous balance and the amount of the payment.

The spreadsheet allows you to copy the formulas doing these calculations into all the appropriate cells of the table, so the remaining table is filled "automatically."

Spreadsheet functions also make it simple to do the sums and differences required to answer parts C and D.

A) see below

B) The beginning balance after 12 payments is $1,476.00.

C) The difference between the original debt and the amount remaining after 12 months is ...

2000 -1476 = 524 . . . dollars

D) The sum of the 12 interest charges is $314.41.