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?

Answer 1

Answer-

The increase in his monthly payment will be $91.44

Solution-

We know that,

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

Where,

PV = present value

P   = periodic payment

r    = rate per period

n   = number of period

1st case-

$PV\ of\ annuity=3750,\\\\P=?,\\\\r = 17.5\%\ annually=\frac{17.5}{12}\%\ monthly=\frac{17.5}{1200}\ monthly\\\\n=12\ months$

Putting the values,

$\Rightarrow 3750=P[\frac{1-(1+\frac{17.5}{1200})^{-12}}{{\frac{17.5}{1200}}}]\\\\\Rightarrow P=\frac{3750}{[\frac{1-(1+\frac{17.5}{1200})^{-12}}{{\frac{17.5}{1200}}}]}\\\\\Rightarrow P=\frac{3750}{\frac{1-0.8405}{0.01458}}\\\\\Rightarrow P=\frac{3750}{\frac{0.1595}{0.01458}}\\\\\Rightarrow P=342.91$

2nd case-

$PV\ of\ annuity=3750+1000=4750,\\\\P=?,\\\\r = 17.5\%\ annually=\frac{17.5}{12}\%\ monthly=\frac{17.5}{1200}\ monthly\\\\n=12\ months$

Putting the values,

$\Rightarrow 4750=P[\frac{1-(1+\frac{17.5}{1200})^{-12}}{{\frac{17.5}{1200}}}]\\\\\Rightarrow P=\frac{4750}{[\frac{1-(1+\frac{17.5}{1200})^{-12}}{{\frac{17.5}{1200}}}]}\\\\\Rightarrow P=\frac{4750}{\frac{1-0.8405}{0.01458}}\\\\\Rightarrow P=\frac{4750}{\frac{0.1595}{0.01458}}\\\\\Rightarrow P=434.35$

The increase in monthly payment will be,

$=434.35-342.91=91.44$

Answer 2

Answer:

b- 91.44

Step-by-step explanation: