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1. This table can be used to organize Raj's credit card balances and payments over 6 months. The annual percentage rate on the card is [tex]18 \%[/tex].

\begin{tabular}{|c|c|c|c|c|}
\hline
\multicolumn{5}{|c|}{Raj's Credit Card Payments} \\
\hline Month & Balance & Payment & Interest Rate & Interest Charged \\
\hline 1 & \[tex]$500 & \$[/tex]100 & 0.015 & \$6.00 \\
\hline 2 & \[tex]$406 & \$[/tex]50 & 0.015 & \\
\hline 3 & \[tex]$361.34 & \$[/tex]50 & 0.015 & \\
\hline 4 & \[tex]$316.01 & \$[/tex]50 & 0.015 & \\
\hline 5 & \[tex]$270 & \$[/tex]50 & 0.015 & \\
\hline 6 & \[tex]$223.30 & \$[/tex]50 & 0.015 & \\
\hline
\end{tabular}

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

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



Answer :

GinnyAnswer
To determine the total interest charged over the first 6 months, follow these steps:

1. Understand the given data:
- Raj's initial balance and the payments he made each month are given.
- The interest rate charge is 1.5% per month.

2. Calculate the interest for each month:
- Month 1:
- Balance = \$500
- Payment = \$100
- Monthly interest rate = 1.5%
- Interest charged = \( \[tex]$500 \times 0.015 = \$[/tex]7.50 \)

- Month 2:
- New Balance = \[tex]$406 (after payment of \$[/tex]100 from month 1)
- Payment = \$50
- Interest charged = \( \[tex]$406 \times 0.015 = \$[/tex]6.09 \)

- Month 3:
- New Balance = \[tex]$361.34 (after payment of \$[/tex]50 from month 2)
- Payment = \$50
- Interest charged = \( \[tex]$361.34 \times 0.015 = \$[/tex]5.42 \)

- Month 4:
- New Balance = \[tex]$316.01 (after payment of \$[/tex]50 from month 3)
- Payment = \$50
- Interest charged = \( \[tex]$316.01 \times 0.015 = \$[/tex]4.74 \)

- Month 5:
- New Balance = \[tex]$270 (after payment of \$[/tex]50 from month 4)
- Payment = \$50
- Interest charged = \( \[tex]$270 \times 0.015 = \$[/tex]4.05 \)

- Month 6:
- New Balance = \[tex]$223.30 (after payment of \$[/tex]50 from month 5)
- Payment = \$50
- Interest charged = \( \[tex]$223.30 \times 0.015 = \$[/tex]3.35 \)

3. Sum up the interest charged over the 6 months:
- Total interest = \( \[tex]$7.50 + \$[/tex]6.09 + \[tex]$5.42 + \$[/tex]4.74 + \[tex]$4.05 + \$[/tex]3.35 = \$31.15 \)

Thus, the total interest charged for the first 6 months is \$31.14975.

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