you have contacted a number of dearlerships to determine the best interest rate on a new car loan, dealship quoted a 5 year, 10% loan in the amount of $35,000 that will require monthly payments. What is the monthly loan payment. And what will the loan effective annual interest rate (EAR)?
To calculate the monthly loan payment, you can use the formula for calculating the monthly payment on a loan:
M = P * (r * (1+r)^n) / ((1+r)^n - 1)
Where:
M = Monthly payment
P = Loan amount ($35,000 in this case)
r = Monthly interest rate (annual interest rate divided by 12)
n = Number of payments (5 years = 60 months)
First, let's calculate the monthly interest rate. The given annual interest rate is 10%, so we divide it by 100 to get the decimal form and then by 12 to get the monthly interest rate:
r = 10% / 100 / 12 = 0.0083333 (rounded to 6 decimal places)
Substituting the values into the formula, we get:
M = 35000 * (0.0083333 * (1+0.0083333)^60) / ((1+0.0083333)^60 - 1)
Calculating this expression will give you the monthly loan payment.
To calculate the loan's effective annual interest rate (EAR), we can use the formula:
EAR = (1 + r)^n - 1
Where:
r is the monthly interest rate (0.0083333)
n is the number of payments (60)
Substituting the values into the formula, we get:
EAR = (1 + 0.0083333)^60 - 1
Calculating this expression will give you the loan's effective annual interest rate.