Suppose a credit card was used to make a
 
​$12 comma 760
 
purchase at 14.9
​% 
interest with a monthly payment of ​$296
. 
Complete the following.
​(a) Calculate the time it will take to pay off the debt making only the given payment each month.
​(b) Calculate the total interest paid.
​(c) Find the amount of money saved over the lifetime of the debt if twice the amount of the given monthly payment is paid each month.
Question content area bottom
Part 1
​(a) If only the given payment  is made each​ month, it will take 63
 
payments to pay off the debt.
​(Round up to the nearest integer as​ needed.)
Part 2
​(b) The total interest paid is ​$5,620.35
.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
Part 3
​(c) The amount of money saved is ​$enter your response here
.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Let's go through the calculations step by step to solve part (c) of the problem, where we want to find how much money is saved if twice the monthly payment is made. We'll break this down into logical parts.

### Step-by-step breakdown:

1. **Original Payment Plan**:
   - Loan amount = $12,760
   - Interest rate = 14.9% annual (monthly interest rate $ r = \frac{14.9}{12} \% = 1.24167\% $)
   - Monthly payment = $296
   - Number of payments (already given) = 63
   - Total interest paid in this plan (given) = $5,620.35

2. **Twice the Monthly Payment Plan**:
   - New monthly payment = $296 \times 2 = $592
   - We will calculate the number of payments required and the interest paid in this case.
   
### Step 1: Calculate the number of payments with the higher payment.

The formula for calculating the number of payments $ n $ when paying off a loan is given by:

\[
n = \frac{-\log(1 - r \frac{P}{M})}{\log(1 + r)}
\]

Where:
- $ r $ is the monthly interest rate (0.0124167)
- $ P $ is the loan amount ($12,760)
- $ M $ is the new monthly payment ($592)

Let's calculate the number of payments.If the monthly payment is doubled to $592, it will take 26 payments to pay off the debt.

### Step 2: Calculate the total interest paid with the higher payment.

The total interest paid is the difference between the total payments made and the original loan amount. Total payments made will be:

\[
\text{Total payments} = M \times n
\]
Where $ M = 592 $ and $ n = 26 $.

We can then calculate the total interest as:

\[
\text{Total interest} = (\text{Total payments}) - P
\]

Let's compute this.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through the remaining calculations manually, or answer any other questions?

Here are some related questions for practice:
1. What is the monthly interest rate if the annual rate is 12%?
2. How does doubling the payment affect the total interest paid on a loan?
3. How can you calculate the total interest paid using an amortization formula?
4. What would happen if you tripled the monthly payment instead?
5. How do interest rates affect the time it takes to repay a loan?

**Tip:** Increasing monthly payments reduces the number of payments, significantly lowering the total interest paid.

Suppose a credit card was used to make a $12,760 purchase at 14.9% interest with a monthly payment of $296. Complete the following. (a) Calculate the time it will take to pay off the debt making only the given payment each month. (b) Calculate the total interest paid. (c) Find the amount of money saved over the lifetime of the debt if twice the amount of the given monthly payment is paid each month.

Learn how to calculate the time it takes to pay off a $12,760 credit card debt with 14.9% interest and a monthly payment of $296. This detailed explanation includes how to find the total interest paid and the savings when doubling the monthly payment.

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