Jessica charges

​$85008500

to a credit card with a

15.6615.66​%

interest rate.

​(a) If Jessica makes a payment of

​$186.18186.18

each​ month, how many payments will it take to retire the​ balance?

​(b) If Jessica doubles the payment to

​$372.36372.36​,

how many payments will it take to retire the​ balance?

​(c) If Jessica pays

​$372.36372.36

each month instead of

​$186.18186.18​,

how much will she save in interest​ charges?

Question content area bottom

Part 1

​(a) It will take

enter your response here

payments to pay off the debt.

​(Round up to the nearest integer as​ needed.)

To solve this, we will use the formula for the number of payments $ N $ required to pay off a loan:

\[
N = \frac{\log \left( \frac{P}{P - r \times B} \right)}{\log(1 + r)}
\]

Where:
- $ B $ is the initial balance of the debt (in this case $ B = 8500 $),
- $ r $ is the monthly interest rate (which is the annual rate divided by 12, so $ r = \frac{15.66}{100 \times 12} = 0.01305 $),
- $ P $ is the monthly payment amount.

### Part (a): Calculate the number of payments when Jessica pays $ 186.18 $ per month

Let’s substitute the values into the formula:

\[
N = \frac{\log \left( \frac{186.18}{186.18 - 0.01305 \times 8500} \right)}{\log(1 + 0.01305)}
\]

We will calculate this step by step.

### Part (b): Calculate the number of payments when Jessica pays $ 372.36 $ per month

Now, substitute $ P = 372.36 $ into the formula:

\[
N = \frac{\log \left( \frac{372.36}{372.36 - 0.01305 \times 8500} \right)}{\log(1 + 0.01305)}
\]

We will calculate this next.

### Part (c): How much will Jessica save in interest charges if she doubles her payment to $ 372.36 $?

The interest saved will be the difference between the total interest paid for the two payment plans.

Total interest paid = (Number of payments × Monthly payment) - Original balance

We will subtract the interest in the doubled payment case from the interest in the original payment case to find the amount saved.

---

I will now calculate each part.### Results:

**(a)** It will take approximately 70 payments (rounded up) for Jessica to pay off the balance when making a monthly payment of $186.18$.

**(b)** If Jessica doubles her payment to $372.36$, it will take approximately 28 payments (rounded up) to pay off the balance.

**(c)** By doubling her monthly payment to $372.36$, Jessica will save about **$2606.52** in interest charges over the duration of the loan.

Would you like more details on any part of the calculations or have any questions? Here are 5 related questions to consider:

1. What if Jessica increases her monthly payment by a smaller amount?
2. How does a lower interest rate impact the number of payments?
3. What if Jessica only paid the minimum interest each month?
4. How can Jessica further minimize her interest charges?
5. What is the effect of compound interest on the total amount paid?

**Tip:** Always aim to pay more than the minimum required on credit card debt to reduce interest charges significantly!

Jessica charges $8500 to a credit card with a 15.66% interest rate. (a) If Jessica makes a payment of $186.18 each month, how many payments will it take to retire the balance? (b) If Jessica doubles the payment to $372.36, how many payments will it take to retire the balance? (c) If Jessica pays $372.36 each month instead of $186.18, how much will she save in interest charges?

Learn how to calculate the number of payments required to pay off a credit card debt with a 15.66% interest rate. Discover how doubling payments can significantly reduce interest charges. This detailed step-by-step solution covers key financial concepts such as loan payment formulas and logarithmic functions. Suitable for high school students and adults managing personal finance.

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