Respuesta :
Answer:
I can pay the loan 58 months faster by making my planned monthly payments of $225 with the new card.
Explanation:
In arriving at the above, I calculated the number of months to make monthly payments using the old card at 130 months and that of the new card as 72 months(as shown in the attached).
Invariably, the difference in months between the two above is 58 months(130-78).
In computing the months I used the nper function in excel as found in the attached spreadsheet
The total time is taken to pay off the loan amount of $ 12,000 is 55.66 months faster than the old credit card.
Calculation of the months to pay off the loan at 19.8 % of the rate:
No of months taken by the old card:
[tex]\begin{aligned}\frac{I}{Y} =\frac{19.8}{12} = 1.65\end{aligned}[/tex]
PMT =$ 225
PV = $ 12,000
FV = 0
[tex]\begin{aligned}\frac{CPT}{N} = 129.56 \:\rm months\end{aligned}[/tex]
No of months taken by new card:
[tex]\begin{aligned}\frac{I}{Y} =\frac{10.4}{12} = 8.6667\end{aligned}[/tex]
PMT =$ 225
PV = $12,000
FV= 0
[tex]\begin{aligned}\frac{CPT}{N} = 71.88 \:\rm months\end{aligned}[/tex]
So, reduced time period (R) :
[tex]\begin{aligned}R = 129.56-71.88\\ = 57.67 \:\rm months\end{aligned}[/tex]
Therefore, it takes 57.67 fewer months to pay off the loan.
Calculation of the months taken to pay off the loan at the 10.4% rate:
If there was a 2% fee charged on balance transferred:
[tex]\begin{aligned}\text{New loan amount} &= \$12,000\times(1+2\%) \\&= \$12,240\end{aligned}[/tex]
No of months taken by new card:
[tex]\begin{aligned}\frac{I}{Y} =\frac{10.4}{12} = 8.6667\end{aligned}[/tex]
PMT= $225
PV = $12,240
FV = 0
[tex]\begin{aligned}\frac{CPT}{N} = 73.89 \:\rm months\end{aligned}[/tex]
So, reduced time period (R):
[tex]\begin{aligned}R = 129.56-73.89 = 55.66 \:\rm months\end{aligned}[/tex]
Therefore, it takes 55.66 fewer months to pay off the loan
To know more about the calculation of the months taken to pay off the loan, refer to the link below:
https://brainly.com/question/8688273
