The table below shows a summary of Amanda's credit card statement for the month of June.

\begin{tabular}{|l|l|}
\hline Transaction types & Amount \\
\hline Unpaid balance from May (Beginning balance on June 1) & [tex]$\$[/tex] 1303.90[tex]$ \\
\hline Purchases made during the month of June & $[/tex]\[tex]$ 288.15$[/tex] \\
\hline Payments made during the month of June & [tex]$\$[/tex] 492.03[tex]$ \\
\hline
\end{tabular}

Complete the parts below. Write your answer to the nearest cent.

(a) Suppose the credit card company charges $[/tex]1.7 \%[tex]$ monthly interest on the unpaid balance from May. How much interest will this be?
$[/tex]\[tex]$ \llbracket$[/tex]

(b) What will Amanda's unpaid balance be on her July 1 statement? (Assume that this balance will include the interest from part (a), but will not include any interest on her June balance yet.)
[tex]$\$[/tex] \square$



Answer :

Let's go through each part of the question step-by-step.

### Part (a): Calculating the Interest on the Unpaid Balance from May
Amanda's unpaid balance from May (beginning balance on June 1) is [tex]\( \$1303.90 \)[/tex]. Her credit card company charges a [tex]\( 1.7\% \)[/tex] monthly interest rate on this balance.

To calculate the interest:

1. Interest Rate Calculation:
The interest rate is [tex]\( 1.7\% \)[/tex]. To use this in monetary calculations, it needs to be converted to a decimal:
[tex]\[ \text{Monthly interest rate} = \frac{1.7}{100} = 0.017 \][/tex]

2. Interest Amount Calculation:
The interest amount charged on the unpaid balance from May is:
[tex]\[ \text{Interest from May} = \text{Beginning balance} \times \text{Monthly interest rate} \][/tex]
Substituting the given values:
[tex]\[ \text{Interest from May} = 1303.90 \times 0.017 \][/tex]
Calculating this gives:
[tex]\[ \text{Interest from May} = \$ 22.17 \][/tex]

Therefore, the interest on the unpaid balance from May is [tex]\(\$22.17\)[/tex].

### Part (b): Calculating the Unpaid Balance on the July 1 Statement
To find Amanda's unpaid balance on her July 1 statement, we need to consider:
- Her beginning balance on June 1
- Interest from the unpaid balance of May
- Purchases made during June
- Payments made during June

The calculation steps are as follows:

1. Add Interest to the Beginning Balance:
[tex]\[ \text{Balance with interest} = \text{Beginning balance} + \text{Interest from May} \][/tex]
Substituting the values gives:
[tex]\[ \text{Balance with interest} = 1303.90 + 22.17 = 1326.07 \][/tex]

2. Add Purchases made during June:
[tex]\[ \text{Total balance with purchases} = \text{Balance with interest} + \text{June purchases} \][/tex]
Substituting the values gives:
[tex]\[ \text{Total balance with purchases} = 1326.07 + 288.15 = 1614.22 \][/tex]

3. Subtract Payments made during June:
[tex]\[ \text{Unpaid balance on July 1} = \text{Total balance with purchases} - \text{June payments} \][/tex]
Substituting the values gives:
[tex]\[ \text{Unpaid balance on July 1} = 1614.22 - 492.03 = 1122.19 \][/tex]

Therefore, Amanda's unpaid balance on her July 1 statement is [tex]\( \$ 1122.19 \)[/tex].

### Final Answers
(a) The interest on the unpaid balance from May is: [tex]\( \boxed{22.17} \)[/tex]

(b) Amanda's unpaid balance on her July 1 statement is: [tex]\( \boxed{1122.19} \)[/tex]