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Andrei [34K]
3 years ago
7

Cesar is excited that he only has 12 months left before he pays off his credit card completely. His current balance is $3,750 an

d 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
Mathematics
2 answers:
Flauer [41]3 years ago
6 0
Just took this test. It's B. $91.44
Lina20 [59]3 years ago
5 0

Answer:

Option B- 91.44 is the correct Answer.

Step-by-step explanation:

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 :

PV of annuity = P=[\frac{1-(1+r)^{-n} }{r}]

PV = Present Value

P   = Periodic payment

r    = rate per period

n   = number of period

case 1 :

PV of annuity = $3,750

P = ?

r = 17.5% annually = \frac{17.5}{12}% monthly \frac{17.5}{1200} monthly

n = 12 months

Now we put the values in formula

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

⇒ P= \frac{3750}{[\frac{1-(1+\frac{17.5}{1200})^{-12}  }{\frac{17.5}{1200} }]}

⇒ P = \frac{3750}{\frac{1-0.8405}{0.01458} }

⇒ P = \frac{3750}{\frac{0.1595}{0.01458} }

⇒ P = 342.91

Case 2 :

PV of annuity = 3750 + 1000 = 4750

P = ?

r = 17.5% annually = \frac{17.5}{12}% monthly = \frac{17.5}{1200} monthly

n = 12 months

Putting the values in formula

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

⇒ P= \frac{4750}{[\frac{1-(1+\frac{17.5}{1200})^{-12}  }{\frac{17.5}{1200} }]}

⇒ P = \frac{4750}{\frac{1-0.8405}{0.01458} }

⇒ P = \frac{4750}{\frac{0.1595}{0.01458} }

⇒ P = 434.35

Cesar's increased monthly payment will be

434.35 - 342.91 = 91.44

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