Suppose Olivia has $6,840 in credit card debt on the VB credit card which has annual interest rate of 18.8%. Olivia is considering transferring her debt to the LA credit card that offers 0% interest for 18 months. If Olivia makes a payment of $380 per month on the VB credit card, what will her balance be at the end of 18 months? Assume that no additional charges are made to the card. (Suggestion: You are trying to find the future value of a debt that has a present value of $6,840. Use the formula for the future value of an ordinary annuity. Round your answer to the nearest cent.)

To solve this, we need to calculate the balance on Olivia's VB credit card after 18 months, given that she pays $380 per month and the card has an annual interest rate of 18.8%. We will use the **future value of an ordinary annuity** formula:

\[
A = P \times \frac{(1 + r)^n - 1}{r}
\]

where:
- $A$ is the future value of the annuity (in this case, the future value of the debt).
- $P$ is the monthly payment amount ($380).
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the number of payments (18 months).

### Step 1: Convert the annual interest rate to a monthly interest rate

The annual interest rate is 18.8%, so the monthly interest rate $r$ is:

\[
r = \frac{18.8\%}{12} = \frac{0.188}{12} = 0.0156667
\]

### Step 2: Use the future value of annuity formula

Now plug in the values:
- $P = 380$
- $r = 0.0156667$
- $n = 18$

\[
A = 380 \times \frac{(1 + 0.0156667)^{18} - 1}{0.0156667}
\]

I'll calculate this to find the future value of the payments made, which will then be subtracted from the initial debt of $6,840 to find the remaining balance.The total amount Olivia would have paid toward her debt over the 18 months, taking into account the interest, is approximately $7,831.64.

### Step 3: Calculate the remaining balance

Olivia's initial debt is $6,840. To find the remaining balance after 18 months, subtract the future value of the payments from the initial debt:

\[
\text{Remaining balance} = 6,840 - 7,831.64
\]

I'll calculate that next.The result is approximately $-\$991.64$, which means that Olivia would have fully paid off her debt after 18 months and would have a surplus of around $991.64. This shows that with her monthly payments of $380, Olivia would clear her debt before the 18-month period ends.

Do you have any questions or would you like more details on any part of the process?

Here are some related questions you might consider:
1. How would the balance change if the interest rate were different?
2. What if Olivia increased her monthly payment?
3. How much interest does Olivia pay over the 18 months?
4. What is the total amount Olivia would pay if she only made minimum payments?
5. How does the future value of debt differ from the future value of savings?

**Tip:** When dealing with loans or credit cards, always check how much interest accrues monthly to understand the total cost over time.

Suppose Olivia has $6,840 in credit card debt on the VB credit card which has an annual interest rate of 18.8%. Olivia is considering transferring her debt to the LA credit card that offers 0% interest for 18 months. If Olivia makes a payment of $380 per month on the VB credit card, what will her balance be at the end of 18 months? Assume that no additional charges are made to the card.

Discover how to calculate the future balance of a $6,840 credit card debt with an 18.8% interest rate and $380 monthly payments over 18 months. Learn the steps using the future value of annuity formula and understand key concepts such as interest rates and debt repayment. Suitable for high school and college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation