SOLUTION: E-Loan, an online lending service, recently offered 48-month auto loans at 5.7% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can

Question 1081394: E-Loan, an online lending service, recently offered 48-month auto loans at 5.7% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $257, how much can you borrow from E-Loan? What is the total interest you will pay for this loan?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
48 month loan at 5.7% compounded monthly with payments of $257 at the end of each month results in a loan amount of $11,007.59

calculator used can be found here:

https://arachnoid.com/finance/

inputs are shown below:

$$$

outputs are shown below:

$$$

time periods are in months.

number of months is 48.

interest rate per month is 5.7% / 12 = .475%

monthly payments are -257.

minus numbers mean money going out and plus numbers mean money coming in.
since you are paying the monthly amount, that number is negative.
the calculator gives you the present value as a positive amount.

you can also solve using the following formula:

in that case, you use the interest rate of .00475 rather than the interest rate percent of .475%.

PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
p = (a*(1-1/(1+r)^n))/r
p is the present value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods.

formula becomes p = (257*(1-1/(1+.00475)^48))/.00475.

you will get the same answer as the calculator provided.

the manual calculations don't require you to make the monthly payments a negative amount.
you enter them as positive amounts and the present value is also a positive amount.

additional formulas can be found here:

https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f5

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