Question

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 1

Just took this test. It's B. $91.44

Answer 2

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