Question

esse Pinkman is thinking about trading cars. He estimates he will still have to borrow ​$31,000 to pay for his new car. How large will​ Jesse's monthly car loan payment be if he can get a ​-year ​( equal monthly​ payments) car loan from the​ university's credit union at an APR of 9.4 percent compounded​ monthly?

Answer 1

Jesse's monthly car loan payment has to be $2,716.75.

Step-by-step explanation:

Jesse's monthly car loan payment can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or amount to borrow = $31,000

P = Monthly car loan payment = ?

r = Monthly interest rate = APR / Number of months in a year = 9.4% / 12 = 0.094 / 12 = 0.00783333333333333

n = Number of months = Number of year * Number of months in a year = 1 * 12 = 12

Substitute the values into equation (1) and solve for P, we have:

$31,000 = P * ((1 - (1 / (1 + 0.00783333333333333))^12) / 0.00783333333333333)

$31,000 = P * 11.4106954292971

P = $31,000 / 11.4106954292971 = $2,716.75

Therefore, Jesse's monthly car loan payment has to be $2,716.75.