1.             You have an unpaid credit card debt of $461.  The interest rate you carry is 17.55%.   Make a table showing Payment Number, Monthly Payment, Balance Less Payment, Plus Interest, and Remaining Balance.  

(A)         Assuming no extra charges, how long will it take to pay off the loan if you make the minimum payment of $25 per month?  

(B)         Would it take exactly half the time to pay off the credit card debt if you doubled up on payments each month?  If not, how much sooner do you pay the debt off in this case when compared to the first case? (Hint: Cut and paste work from (A) but change the amount that you are paying per month to $50 based on this problem.)  
  
(C)         Determine the amount of interest paid in (A).  Determine the amount of interest paid in (B).  Determine how much you save in interest when you double up on the payments. (Hint: Add up the amounts in the Plus Interest columns for (A) and then add up the same for (B) The difference between those values tells you how much interest you saved.)  

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.

---

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**.

---

### (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

You have an unpaid credit card debt of $461. The interest rate you carry is 17.55%. Make a table showing Payment Number, Monthly Payment, Balance Less Payment, Plus Interest, and Remaining Balance.
(A) Assuming no extra charges, how long will it take to pay off the loan if you make the minimum payment of $25 per month?
(B) Would it take exactly half the time to pay off the credit card debt if you doubled up on payments each month? If not, how much sooner do you pay the debt off in this case when compared to the first case?
(C) Determine the amount of interest paid in (A). Determine the amount of interest paid in (B). Determine how much you save in interest when you double up on the payments.

Explore how long it takes to pay off a $461 credit card debt at a 17.55% interest rate with a $25 monthly payment vs. doubling the payment to $50. This guide covers interest calculation, loan repayment time, and how much interest you save by paying more each month. Suitable for Grades 10-12.

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