Question

E-Loan, an online lending service, recently offered 48-month auto loans at 4.2% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $360, how much can you borrow from E-Loan? What is the total interest you will pay for this loan? You can borrow $(Round to two decimal places.) You will pay a total of Sin interest. (Round to two decimal places.) As Enter your answer in each of the answer boxes.

Please give me complete details on how to do this.

Answer 1

We can use the present value of the annuity formula to find the amount of loan.

$\small \textup{PVA} = \textup{A}\left [\frac{(1-(1+i)^{-n})}{i} \right ]$

Where,
PVA = Present value of the annuity
A = Annuity or payment
i = Monthly interest rate in decimal form
n = Number of months

i = 4.2% / 2 = 0.35% = 0.0035

Therefore,

$\small \textup{PVA} = \textup{360}\left [\frac{(1-(1+0.0035)^{-48})}{0.0035} \right ]$

= 360 1 -0.845G0183 0.0035

$\small = \textup{360}\left [\frac{0.15439817}{0.0035} \right ]$

$\small = \textup{360}\times (44.11376)$

$\small = \$$15,880.95$

Therefore, the amount of loan = $15,880.95

Total amount paid = 360 * 48 =  $17,280.00

Therefore,

Interest paid = Total amount paid - Amount of loan

=  $17,280.00 - $15,880.95

= $1,399.05