Final answer:
To fully pay off the debt by making a $100 payment first and then $20 payments each month, it would take 5 months. The total amount of money saved would be $300.
Step-by-step explanation:
To calculate the time and money saved by making a $100 payment first and then $20 payments each month, we need to set up an equation. Let's assume the original amount owed is P. The equation would be:
P = 100 + 20t
Where t is the number of months after the first month. The interest rate stays at 22% as long as there are no missed payments in month 7. To find the total time and money saved, we need to find the minimum value of t that would make the balance equal to 0.
By substituting the equation into the balance equation, we get 100 + 20t = P. Since we are assuming the original amount owed is P, we set P to 0 and solve for t.
0 = 100 + 20t
-100 = 20t
t = -100/20
t = -5
The negative value for t doesn't make sense in this context, so we can ignore it. Therefore, it would take 5 months to fully pay off the debt.
To find the total amount of money saved, we can calculate the total payments made in those 5 months. Each month, $20 is deducted from the remaining balance. So, the total payments made would be:
Total payments = 100 + 20(1) + 20(2) + 20(3) + 20(4) + 20(5) = $300
Therefore, by making the initial $100 payment and then $20 payments each month, you would save $300 in total payments compared to paying off the debt without making any payments.
Learn more about How to save money by making monthly payments instead of paying off the debt in one go.