Jesse Pinkman is considering taking out a car loan of $26,000 to purchase a new car. He has the option to get a 4-year car loan from the university's credit union with an Annual Percentage Rate (APR) of 9.5 percent, compounded monthly. He wants to know how much his monthly car loan payment will be.
To calculate Jesse's monthly car loan payment, we can use the formula for calculating the monthly payment on a loan:
PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate
n = Number of payments
In this case, the principal amount (P) is $26,000, the annual interest rate is 9.5 percent, compounded monthly. To find the monthly interest rate (r), we divide the annual interest rate by 12 (number of months in a year) and then divide by 100 to convert it to a decimal: r = (9.5 / 12) / 100 = 0.0079167
The number of payments (n) is 48, as it is a 4-year loan with 48 equal monthly payments. Now we can plug these values into the formula to calculate the monthly car loan payment (PMT): PMT = (26,000 * 0.0079167 * (1 + 0.0079167 )^48) / ((1 + 0.0079167 )^48 - 1). PMT ≈ $653.20 (rounded to the nearest cent). Jesse's monthly car loan payment will be approximately $653.20. This means that Jesse will need to pay $653.20 every month for 48 months to fully pay off his car loan of $26,000.
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