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Sagot :
To find the total interest charged over the first 6 months for Gigi's credit card, let’s follow a step-by-step process of calculating the interest for each month and fill in the details in the provided table:
1. Month 1:
- Balance: \[tex]$650.00 - Payment: \$[/tex]300.00
- Interest Rate: 0.01167 (monthly interest rate)
- Interest Charged: \[tex]$650 * 0.01167 = \$[/tex]7.5855
- New Balance after payment and interest: \[tex]$650 - \$[/tex]300 + \[tex]$7.5855 = \$[/tex]357.5855
Update the table:
[tex]\[ \begin{aligned} &\text{1} & & \$650 & & \$300 & & 0.01167 & & \$ 7.5855 \\ \end{aligned} \][/tex]
2. Month 2:
- Balance: \[tex]$357.5855 (carried from previous month) - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$357.5855 * 0.01167 = \$[/tex]4.1730
- New Balance: \[tex]$357.5855 - \$[/tex]50 + \[tex]$4.1730 = \$[/tex]311.7585
Update the table:
[tex]\[ \begin{aligned} &\text{2} & & \$357.5855 & & \$50 & & 0.01167 & & \$ 4.1730 \\ \end{aligned} \][/tex]
3. Month 3:
- Balance: \[tex]$311.7585 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$311.7585 * 0.01167 = \$[/tex]3.6382
- New Balance: \[tex]$311.7585 - \$[/tex]50 + \[tex]$3.6382 = \$[/tex]265.3967
Update the table:
[tex]\[ \begin{aligned} &\text{3} & & \$311.7585 & & \$50 & & 0.01167 & & \$ 3.6382 \\ \end{aligned} \][/tex]
4. Month 4:
- Balance: \[tex]$265.3967 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$265.3967 * 0.01167 = \$[/tex]3.0972
- New Balance: \[tex]$265.3967 - \$[/tex]50 + \[tex]$3.0972 = \$[/tex]218.4939
Update the table:
[tex]\[ \begin{aligned} &\text{4} & & \$265.3967 & & \$50 & & 0.01167 & & \$ 3.0972 \\ \end{aligned} \][/tex]
5. Month 5:
- Balance: \[tex]$218.4939 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$218.4939 * 0.01167 = \$[/tex]2.5498
- New Balance: \[tex]$218.4939 - \$[/tex]50 + \[tex]$2.5498 = \$[/tex]171.0437
Update the table:
[tex]\[ \begin{aligned} &\text{5} & & \$218.4939 & & \$50 & & 0.01167 & & \$ 2.5498 \\ \end{aligned} \][/tex]
6. Month 6:
- Balance: \[tex]$171.0437 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$171.0437 * 0.01167 = \$[/tex]1.9961
- New Balance: \[tex]$171.0437 - \$[/tex]50 + \[tex]$1.9961 = \$[/tex]123.0398
Update the table:
[tex]\[ \begin{aligned} &\text{6} & & \$171.0437 & & \$50 & & 0.01167 & & \$ 1.9961 \\ \end{aligned} \][/tex]
To find the total interest charged over the 6 months, sum up the monthly interests:
[tex]\[ 7.5855 + 4.1730 + 3.6382 + 3.0972 + 2.5498 + 1.9961 = 23.0398 \][/tex]
So, the total interest charged over the first 6 months is \$23.04.
Therefore, the amount of interest charged for the first 6 months is [tex]\(\boxed{23.04}\)[/tex].
1. Month 1:
- Balance: \[tex]$650.00 - Payment: \$[/tex]300.00
- Interest Rate: 0.01167 (monthly interest rate)
- Interest Charged: \[tex]$650 * 0.01167 = \$[/tex]7.5855
- New Balance after payment and interest: \[tex]$650 - \$[/tex]300 + \[tex]$7.5855 = \$[/tex]357.5855
Update the table:
[tex]\[ \begin{aligned} &\text{1} & & \$650 & & \$300 & & 0.01167 & & \$ 7.5855 \\ \end{aligned} \][/tex]
2. Month 2:
- Balance: \[tex]$357.5855 (carried from previous month) - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$357.5855 * 0.01167 = \$[/tex]4.1730
- New Balance: \[tex]$357.5855 - \$[/tex]50 + \[tex]$4.1730 = \$[/tex]311.7585
Update the table:
[tex]\[ \begin{aligned} &\text{2} & & \$357.5855 & & \$50 & & 0.01167 & & \$ 4.1730 \\ \end{aligned} \][/tex]
3. Month 3:
- Balance: \[tex]$311.7585 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$311.7585 * 0.01167 = \$[/tex]3.6382
- New Balance: \[tex]$311.7585 - \$[/tex]50 + \[tex]$3.6382 = \$[/tex]265.3967
Update the table:
[tex]\[ \begin{aligned} &\text{3} & & \$311.7585 & & \$50 & & 0.01167 & & \$ 3.6382 \\ \end{aligned} \][/tex]
4. Month 4:
- Balance: \[tex]$265.3967 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$265.3967 * 0.01167 = \$[/tex]3.0972
- New Balance: \[tex]$265.3967 - \$[/tex]50 + \[tex]$3.0972 = \$[/tex]218.4939
Update the table:
[tex]\[ \begin{aligned} &\text{4} & & \$265.3967 & & \$50 & & 0.01167 & & \$ 3.0972 \\ \end{aligned} \][/tex]
5. Month 5:
- Balance: \[tex]$218.4939 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$218.4939 * 0.01167 = \$[/tex]2.5498
- New Balance: \[tex]$218.4939 - \$[/tex]50 + \[tex]$2.5498 = \$[/tex]171.0437
Update the table:
[tex]\[ \begin{aligned} &\text{5} & & \$218.4939 & & \$50 & & 0.01167 & & \$ 2.5498 \\ \end{aligned} \][/tex]
6. Month 6:
- Balance: \[tex]$171.0437 - Payment: \$[/tex]50.00
- Interest Charged: \[tex]$171.0437 * 0.01167 = \$[/tex]1.9961
- New Balance: \[tex]$171.0437 - \$[/tex]50 + \[tex]$1.9961 = \$[/tex]123.0398
Update the table:
[tex]\[ \begin{aligned} &\text{6} & & \$171.0437 & & \$50 & & 0.01167 & & \$ 1.9961 \\ \end{aligned} \][/tex]
To find the total interest charged over the 6 months, sum up the monthly interests:
[tex]\[ 7.5855 + 4.1730 + 3.6382 + 3.0972 + 2.5498 + 1.9961 = 23.0398 \][/tex]
So, the total interest charged over the first 6 months is \$23.04.
Therefore, the amount of interest charged for the first 6 months is [tex]\(\boxed{23.04}\)[/tex].
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