cesar is excited that he only has 12 months left before he pays off his credit card completely. his current…

cesar is excited that he only has 12 months left before he pays off his credit card completely. his current balance is $3,750 and his apr is 17.5%. but when he is involved in a car accident, he is forced to use his credit card to pay a $1,000 deductible to get his car fixed. how much will cesars minimum monthly payment increase if he still wants to pay off his credit card in 12 months?\na. $83.33\nb. $91.44\nc. $342.91\nd. $434.35\nplease select the best answer from the choices provided\no a\no b\no c\no d

cesar is excited that he only has 12 months left before he pays off his credit card completely. his current balance is $3,750 and his apr is 17.5%. but when he is involved in a car accident, he is forced to use his credit card to pay a $1,000 deductible to get his car fixed. how much will cesars minimum monthly payment increase if he still wants to pay off his credit card in 12 months?\na. $83.33\nb. $91.44\nc. $342.91\nd. $434.35\nplease select the best answer from the choices provided\no a\no b\no c\no d

Answer

Explanation:

Step1: Calculate the monthly interest rate

The annual percentage rate (APR) is (17.5%). The monthly interest rate (r=\frac{0.175}{12})

Step2: Use the formula for the monthly payment of a loan

The formula for the monthly payment (M) of a loan with present value (PV), number of months (n) and monthly interest rate (r) is (M = PV\times\frac{r(1 + r)^{n}}{(1 + r)^{n}-1})

Case 1: Initial balance (PV_1 = 3750), (n = 12), (r=\frac{0.175}{12})

[ \begin{align*} M_1&=3750\times\frac{\frac{0.175}{12}(1+\frac{0.175}{12})^{12}}{(1+\frac{0.175}{12})^{12}-1}\ \end{align*} ] [ \begin{align*} (1+\frac{0.175}{12})^{12}&=\left(\frac{12 + 0.175}{12}\right)^{12}=\left(\frac{12.175}{12}\right)^{12}\approx1.1903\ \frac{0.175}{12}(1+\frac{0.175}{12})^{12}&\approx\frac{0.175}{12}\times1.1903\approx0.0173\ (1+\frac{0.175}{12})^{12}-1&\approx1.1903 - 1=0.1903\ M_1&=3750\times\frac{0.0173}{0.1903}\approx3750\times0.0909\approx340.88 \end{align*} ]

Case 2: New balance (PV_2=3750 + 1000=4750), (n = 12), (r=\frac{0.175}{12})

[ \begin{align*} M_2&=4750\times\frac{\frac{0.175}{12}(1+\frac{0.175}{12})^{12}}{(1+\frac{0.175}{12})^{12}-1}\ \end{align*} ] [ \begin{align*} M_2&=4750\times\frac{0.0173}{0.1903}\approx4750\times0.0909\approx431.78 \end{align*} ]

Step3: Calculate the increase in monthly payment

The increase (\Delta M=M_2 - M_1) [ \begin{align*} \Delta M&\approx431.78- 340.88\ &\approx90.9\approx91.44 \end{align*} ]

Answer:

B. ($91.44)