pdmull77
Answered

Benjamin's credit card has an APR of [tex]$19\%$[/tex], calculated on the previous monthly balance, and a minimum payment of [tex]$2\%$[/tex], starting the month after the first purchase. His credit card record for the last 7 months is shown in the table below.

\begin{tabular}{ccccccc}
\hline
\begin{tabular}{c}
End of \\
month
\end{tabular} &
\begin{tabular}{c}
Previous \\
balance
\end{tabular} &
\begin{tabular}{c}
New \\
charges
\end{tabular} &
\begin{tabular}{c}
Payment \\
received
\end{tabular} &
\begin{tabular}{c}
Finance \\
charges
\end{tabular} &
\begin{tabular}{c}
Principal \\
paid
\end{tabular} &
\begin{tabular}{c}
New \\
balance
\end{tabular} \\
\hline
1 & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 2400.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 2400.00$[/tex] \\
2 & [tex]$\$[/tex] 2400.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 48.00[tex]$ & $[/tex]\[tex]$ 38.00$[/tex] & [tex]$\$[/tex] 10.00[tex]$ & $[/tex]\[tex]$ 2390.00$[/tex] \\
3 & [tex]$\$[/tex] 2390.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 47.80[tex]$ & $[/tex]\[tex]$ 37.84$[/tex] & [tex]$\$[/tex] 9.96[tex]$ & $[/tex]\[tex]$ 2380.04$[/tex] \\
4 & [tex]$\$[/tex] 2380.04[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 47.60[tex]$ & $[/tex]\[tex]$ 37.68$[/tex] & [tex]$\$[/tex] 9.92[tex]$ & $[/tex]\[tex]$ 2370.12$[/tex] \\
5 & [tex]$\$[/tex] 2370.12[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 47.40[tex]$ & $[/tex]\[tex]$ 37.53$[/tex] & [tex]$\$[/tex] 9.88[tex]$ & $[/tex]\[tex]$ 2360.25$[/tex] \\
6 & [tex]$\$[/tex] 2360.25[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 47.20[tex]$ & $[/tex]\[tex]$ 37.37$[/tex] & [tex]$\$[/tex] 9.83[tex]$ & $[/tex]\[tex]$ 2350.41$[/tex] \\
7 & [tex]$\$[/tex] 2350.41[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 47.01[tex]$ & $[/tex]\[tex]$ 37.21$[/tex] & [tex]$\$[/tex] 9.79[tex]$ & $[/tex]\[tex]$ 2340.62$[/tex] \\
\hline
\end{tabular}

What is the total amount that Benjamin has made in payments over the 7 months?

A. [tex]$\$[/tex] 47.01[tex]$

B. $[/tex]\[tex]$ 225.64$[/tex]

C. [tex]$\$[/tex] 59.38[tex]$

D. $[/tex]\[tex]$ 285.01$[/tex]



Answer :

GinnyAnswer
To determine the total amount that Benjamin has made in payments over the 7 months, we need to sum the individual payments he made at the end of each month.

Based on the credit card record provided in the table:

- At the end of month 1: Payment = [tex]$0.00 - At the end of month 2: Payment = $[/tex]48.00
- At the end of month 3: Payment = [tex]$47.80 - At the end of month 4: Payment = $[/tex]47.60
- At the end of month 5: Payment = [tex]$47.40 - At the end of month 6: Payment = $[/tex]47.20
- At the end of month 7: Payment = $47.01

We add these amounts together to find the total payments over the 7 months:

[tex]\[ 0.00 + 48.00 + 47.80 + 47.60 + 47.40 + 47.20 + 47.01 = 285.01 \][/tex]

Therefore, the total amount that Benjamin has made in payments over the 7 months is:

[tex]\[ \boxed{285.01} \][/tex]