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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 Cesar’s minimum monthly payment increase if he still wants to pay off his credit card in 12 months? a. $83. 33 b. $91. 44 c. $342. 91 d. $434. 35.

Answer :

shubhamchouhanvrVT

The amount by Cesar’s minimum monthly payment increase will be $91.44.

What will be the amount?

Cesar only has 12 months left before he pays off his credit card completely.

His current balance = $3,750

                       APR = 17.5%

Now we use the formula :

[tex]\rm Present \ value \ of \ anuity= P=( 1-\frac{1+r}{r} })^{-n}[/tex]

PV = Present Value

P   = Periodic payment

r    = rate per period

n   = number of period

Now for the first case:

PV of annuity = $3,750

P =?

r = 17.5% annually = % monthly  monthly

n = 12 months

Now we put the values in the formula

[tex]3750=P(1-\dfrac{(1+\dfrac{17.5}{1200})^{-12}}{\dfrac{17.5}{1200} } )[/tex]

[tex]P=\dfrac{3750}{\dfrac{1-0.8405}{0.01458} }[/tex]

[tex]P=342.91[/tex]

Now for the second Case :

PV of annuity = 3750 + 1000 = 4750

P =?

r = 17.5% annually = % monthly =  monthly

n = 12 months

Putting the values in the formula

[tex]4750=P(1-\dfrac{(1+\dfrac{17.5}{1200})^{-12}}{\dfrac{17.5}{1200} } )[/tex]

[tex]P=\dfrac{4750}{1-\dfrac{1+\frac{17.5}{1200} }{\frac{17.5}{1200} } }[/tex]

[tex]P=\dfrac{4750}{\dfrac{0.1595}{0.01458} } =434.35[/tex]

Cesar's increased monthly payment will be

434.35 - 342.91 = 91.44

Hence, the amount by Cesar’s minimum monthly payment increase will be $91.44.

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