To determine the new balance at the end of month 7 on Lanny's credit card, we need to consider four components:
1. Previous balance: This is the balance from the previous month, which is [tex]$74.33.
2. New charges: These are the new purchases or charges added to the account, which amount to $[/tex]99.00.
3. Payment received: This is the payment that Lanny made towards the credit card, which is [tex]$91.98.
4. Finance charges: These are the interest charges that accrued over the month, amounting to $[/tex]2.04.
To find the new balance, we follow these steps:
1. Start with the previous balance.
2. Add the new charges to the previous balance.
3. Add the finance charges to the total from step 2.
4. Subtract the payment received from the total in step 3.
Summarizing these steps mathematically:
[tex]\[ \text{New balance} = \text{Previous balance} + \text{New charges} + \text{Finance charges} - \text{Payment received} \][/tex]
Let's plug in the values:
[tex]\[
\text{New balance} = 74.33 + 99.00 + 2.04 - 91.98
\][/tex]
After performing the operations sequentially, we get:
[tex]\[
74.33 + 99.00 = 173.33
\][/tex]
[tex]\[
173.33 + 2.04 = 175.37
\][/tex]
[tex]\[
175.37 - 91.98 = 83.39
\][/tex]
Therefore, the new balance at the end of month 7 is [tex]$83.39.
So the correct answer is:
D. $[/tex]\[tex]$83.39$[/tex]
