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]
