Your credit card has a balance of $2800 and an annual interest rate of 12%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, you must pay $93.00 each month, and you will pay a total interest of $548.00. Assume you decide to pay off the balance over one year rather than three. How much more must you pay each month and how much less will you pay in total interest?
If you decide to pay off the balance over one year rather than three, you would be paying off the balance in a shorter period of time. This means you would have to pay more each month in order to pay off the balance in one year.
To calculate how much more you must pay each month, we can set up an equation based on the total interest paid in each scenario.
In the three-year scenario, you pay a total interest of $548 over the course of 36 months.
In the one-year scenario, you would be paying off the balance in 12 months. Let x be the additional amount you must pay each month in order to pay off the balance in one year. This means each monthly payment would be $93 + x.
The total interest paid in the one-year scenario can be calculated by multiplying the number of months (12) by the monthly payment ($93 + x), and subtracting the original balance ($2800). This should be equal to the total interest of $548 paid in the three-year scenario:
12(93 + x) - 2800 = 548
Expanding the left-hand side of the equation gives:
1116 + 12x - 2800 = 548
Rearranging this equation gives:
12x = 2232
Dividing both sides by 12 gives:
x = 186
Therefore, in the one-year scenario, you must pay $186 more each month. This means you would be paying a total of $279 ($93 + $186) each month.
To calculate how much less you will pay in total interest, we can compare the total interest paid in the one-year scenario to the total interest paid in the three-year scenario.
Total interest paid in one-year scenario:
12(93 + 186) - 2800 = 2120
In conclusion, if you decide to pay off the balance over one year rather than three, you would need to pay $279 each month, $186 more than in the three-year scenario, and you will pay $2120 in total interest, $428 less than in the three-year scenario.