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This table can be used to organize Gigi's credit card balances and payments over 6 months. The annual percentage rate on the credit card is [tex]$14 \%$[/tex].

\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{ Gigi's Credit Card Payments } \\
\hline Month & Balance & Payment & Interest Rate & Interest Charged \\
\hline 1 & [tex]$\$[/tex] 650[tex]$ & $[/tex]\[tex]$ 300$[/tex] & 0.01167 & [tex]$\$[/tex] 4.08[tex]$ \\
\hline 2 & $[/tex]\[tex]$ 354.08$[/tex] & [tex]$\$[/tex] 50[tex]$ & 0.01167 & \\
\hline 3 & $[/tex]\[tex]$ 307.63$[/tex] & [tex]$\$[/tex] 50[tex]$ & 0.01167 & \\
\hline 4 & $[/tex]\[tex]$ 260.64$[/tex] & [tex]$\$[/tex] 50[tex]$ & 0.01167 & \\
\hline 5 & $[/tex]\[tex]$ 213.10$[/tex] & [tex]$\$[/tex] 50[tex]$ & 0.01167 & \\
\hline 6 & $[/tex]\[tex]$ 165$[/tex] & [tex]$\$[/tex] 50[tex]$ & 0.01167 & \\
\hline \hline
\end{tabular}

What is the amount of interest charged for the first 6 months?

$[/tex]\[tex]$[/tex] [tex]$\square$[/tex]

Sagot :

GinnyAnswer
To determine the total amount of interest charged on Gigi's credit card over the first six months, we can break down the balance, payments, and interest charges for each month step-by-step.

### Starting Balance and Interest Rate
- Balance Month 1: \[tex]$650 - Annual Percentage Rate: 14% - Monthly Interest Rate: 0.01167 (given) ### Month 1 - Balance: \$[/tex]650
- Payment: \[tex]$300 - Interest Charged: \$[/tex]650 * 0.01167 ≈ \[tex]$4.08 ### Month 2 - New Balance: \$[/tex]650 - \[tex]$300 + \$[/tex]4.08 = \[tex]$354.08 - Payment: \$[/tex]50
- Interest Charged: \[tex]$354.08 * 0.01167 ≈ \$[/tex]4.13

### Month 3
- New Balance: \[tex]$354.08 - \$[/tex]50 + \[tex]$4.13 = \$[/tex]308.21
- Payment: \[tex]$50 - Interest Charged: \$[/tex]308.21 * 0.01167 ≈ \[tex]$3.60 ### Month 4 - New Balance: \$[/tex]308.21 - \[tex]$50 + \$[/tex]3.60 = \[tex]$261.81 - Payment: \$[/tex]50
- Interest Charged: \[tex]$261.81 * 0.01167 ≈ \$[/tex]3.06

### Month 5
- New Balance: \[tex]$261.81 - \$[/tex]50 + \[tex]$3.06 = \$[/tex]214.87
- Payment: \[tex]$50 - Interest Charged: \$[/tex]214.87 * 0.01167 ≈ \[tex]$2.51 ### Month 6 - New Balance: \$[/tex]214.87 - \[tex]$50 + \$[/tex]2.51 = \[tex]$167.38 - Payment: \$[/tex]50
- Interest Charged: \[tex]$167.38 * 0.01167 ≈ \$[/tex]1.95

### Summing Up Interest Charges
- Month 1: \[tex]$4.08 - Month 2: \$[/tex]4.13
- Month 3: \[tex]$3.60 - Month 4: \$[/tex]3.06
- Month 5: \[tex]$2.51 - Month 6: \$[/tex]1.95

Total Interest Charged over the first 6 months:
[tex]\[ \$4.08 + \$4.13 + \$3.60 + \$3.06 + \$2.51 + \$1.95 \approx 23.03 \][/tex]

Thus, the total amount of interest charged over the first 6 months is:
[tex]\[ \$23.03 \][/tex]
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