A student opens a credit card and immediately maxes it out by putting $500 on it in order to pay for their spring break trip. The credit card has an interest rate of 25.99%, and the interest is compounded monthly. If the student doesn't make any payments for the first 12 months that they have the credit card, what will be the balance on the card rounded to the nearest penny? Use either nt A = P(1+ )“ or A = Pe". $

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Scenario:**

A student opens a credit card and immediately maxes it out by putting **$500** on it in order to pay for their spring break trip. The credit card has an interest rate of **25.99%**, and the interest is compounded monthly. If the student doesn’t make any payments for the first **12** months that they have the credit card, what will be the balance on the card rounded to the nearest penny?

**Given Formulas:**

You can calculate the balance using either of the following formulas:

1. \( A = P \left(1 + \frac{r}{n}\right)^{nt} \)

2. \( A = Pe^{rt} \)

**Symbols Explanation:**

- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (initial amount).
- \( r \) = annual interest rate (as a decimal).
- \( n \) = number of times that interest is compounded per year.
- \( t \) = the time the money is invested for in years.
- \( e \) = Euler's number (approximately 2.71828).

**Task:**

Calculate the balance on the credit card after 12 months.
Transcribed Image Text:**Problem Scenario:** A student opens a credit card and immediately maxes it out by putting **$500** on it in order to pay for their spring break trip. The credit card has an interest rate of **25.99%**, and the interest is compounded monthly. If the student doesn’t make any payments for the first **12** months that they have the credit card, what will be the balance on the card rounded to the nearest penny? **Given Formulas:** You can calculate the balance using either of the following formulas: 1. \( A = P \left(1 + \frac{r}{n}\right)^{nt} \) 2. \( A = Pe^{rt} \) **Symbols Explanation:** - \( A \) = the amount of money accumulated after n years, including interest. - \( P \) = the principal amount (initial amount). - \( r \) = annual interest rate (as a decimal). - \( n \) = number of times that interest is compounded per year. - \( t \) = the time the money is invested for in years. - \( e \) = Euler's number (approximately 2.71828). **Task:** Calculate the balance on the credit card after 12 months.
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