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Sagot :
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]
### 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]
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