Question

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

Answer 1

Lucy is expected to be charged by the interest amount of $\boxed{\ \:9.75}$ 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 $SI$ on the principal amount $P$ at rate percentage $r$ for time duration of $t$ years is calculated by the formula as shown below.

$\boxed{SI = \frac{{P \cdot r \cdot t}}{{100}}}$

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

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 $\dfrac{1}{12}$ years.

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

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

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

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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.

Answer 2

$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.

$\boxed{ \ I = P \times r \times t \ }$  

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 $\frac{18}{100}$ or 0.18  
• t = $\frac{1}{12}$ year  (one month)

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

$\boxed{ \ = 650 \times \frac{18}{100} \times \frac{1}{12} \ }$  

$\boxed{ \ = 65 \times \frac{3}{10} \times \frac{1}{2} \ }$  

$\boxed{ \ = \frac{195}{10} \times \frac{1}{2} \ }$  

$\boxed{ \ = \frac{97.5}{10} \ }$  

$\boxed{ \ = \frac{975}{100} \ }$  

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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