To solve this problem, we need to first understand how credit card interest works. Each month, after the payment is made, the remaining balance is subject to an interest charge, calculated using the annual interest rate divided by 12. In this case, the interest rate is 17.55%, so the monthly interest rate will be:

$\text{Monthly interest rate} = \frac{17.55\%}{12} = \frac{17.55}{12} = 1.4625\%$

Let's approach this problem in three steps:

Step 1: Scenario (A) - Minimum Monthly Payment of $25

We will build a table showing the progression of the debt repayment assuming you make a $25 payment each month.

Payment Number	Monthly Payment	Balance Before Payment	Interest	Remaining Balance
1	$25	$461	?	?
2	$25	?	?	?
...	...	...	...	...
n	$25	0	?	0

We will apply the formula for calculating interest each month as:

$\text{Interest} = \text{Remaining Balance} \times \frac{17.55}{12} \times 100$

Then we calculate how many months it takes to fully pay off the debt.

Step 2: Scenario (B) - Doubling the Payment to $50

We repeat the same process, but this time, we increase the monthly payment to $50. We will determine whether this strategy takes half the time or less, and how much sooner the debt is repaid.

Step 3: Interest Savings Calculation

For both scenarios, we sum the total interest paid over the duration of the repayment period. The difference between the interest amounts will give us the savings due to doubling the payments.

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I will now compute the exact values for each scenario.### (A) Minimum Monthly Payment of $25

For Scenario (A), where the monthly payment is $25:

Payment Number	Monthly Payment	Balance Before Payment	Interest	Remaining Balance
1	$25	$461	$6.74	$442.74
2	$25	$442.74	$6.48	$424.22
3	$25	$424.22	$6.20	$405.42
...	...	...	...	...
22	$25	$15.96	$0.23	$0

It will take 22 months to pay off the credit card debt. The total interest paid over this period is $80.19.

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(B) Doubling the Payment to $50

For Scenario (B), where the monthly payment is $50:

Payment Number	Monthly Payment	Balance Before Payment	Interest	Remaining Balance
1	$50	$461	$6.74	$417.74