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If the typical balance on Lucy's credit card is $650 and the interest rate (APR) on her credit card is 18%, how much in interest would you expect Lucy to be charged in a typical month

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BladeRunner212

$9.75

Further explanation  

Given:  

  • The typical balance on Lucy's credit card is $650.
  • The interest rate (APR) on her credit card is 18%.

Question:  

How much in interest would you expect Lucy to be charged in a typical month?

The Process:  

This problem includes the type of determining simple interest.

[tex]\boxed{ \ I = P \times r \times t \ }[/tex]  

where,

  • I = simple interest
  • P = principal (initial amount)  
  • r = annual interest rate
  • t = time (in years)

This time we will find out how much in interest we would expect to be charged in a typical month.

The data is as follows:

  • P = 650
  • r = 18% or [tex]\frac{18}{100}[/tex] or 0.18  
  • t = [tex]\frac{1}{12}[/tex] year  (one month)

Let us calculate how much in interest we would expect to be charged in a typical month.

[tex]\boxed{ \ = 650 \times \frac{18}{100} \times \frac{1}{12} \ }[/tex]  

[tex]\boxed{ \ = 65 \times \frac{3}{10} \times \frac{1}{2} \ }[/tex]  

[tex]\boxed{ \ = \frac{195}{10} \times \frac{1}{2} \ }[/tex]  

[tex]\boxed{ \ = \frac{97.5}{10} \ }[/tex]  

[tex]\boxed{ \ = \frac{975}{100} \ }[/tex]  

Thus the amount of interest we would expect Lucy to be charged in a typical month is $ 9.75.

_ _ _ _ _ _ _ _ _ _

Notes  

We must be able to distinguish between simple and compound interest. Please learn about this in the link attached below.

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Lucy is expected to be charged by the interest amount of [tex]\boxed{\$\:9.75}[/tex] in a month.

Explanation:

The simple interest is the interest that is charged on loan amounts or any other payments made which are lapsed for certain time duration.

The simple interest [tex]SI[/tex] on the principal amount [tex]P[/tex] at rate percentage [tex]r[/tex] for time duration of [tex]t[/tex] years is calculated by the formula as shown below.

[tex]\boxed{SI = \frac{{P \cdot r \cdot t}}{{100}}}[/tex]

The typical balance on Lucy’s credit card is [tex]\$\:650[/tex] so the interest has to be charged on this value only. Hence, the principal amount is [tex]\$\:650[/tex].

There are 12 months in a year so if the interest is charged as per month basis, the time of one month is taken as [tex]\dfrac{1}{12}[/tex] years.

Substitute 650 for [tex]P[/tex], \frac{1}{12} for [tex]t[/tex] and 18 for [tex]r[/tex] to obtain the interest charged at a rate of 18% per annum.

[tex]\boxed{\begin{aligned}{\text{Interest charged}} &=\frac{P\cdot r\cdot t}{100}\\&= \frac{{650 \cdot 18 \cdot \frac{1}{{12}}}}{{100}} \\ &= \frac{{65 \cdot 18}}{{120}} \\& = 9.75\end{aligned}}[/tex]

Thus, the interest charged at Lucy’s credit card is [tex]\boxed{\$\:9.75}[/tex] per month.

Learn More:

1. Learn more about algebraic expression https://brainly.com/question/5533462

2. Learn more about linear equation application https://brainly.com/question/2479097

3. Learn more about equations https://brainly.com/question/2788996

Answer Details:

Grade: Middle School

Subject: Mathematics

Chapter: Simple Interest

Keywords: simple interest, interest, rate, time duration, months, years, rate percentage, principal, amount, credit card, Lucy.

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