You want to purchase a car, and a bank is willing to lend you $15,000. The loan will be fully amortized over 5 years (60 months), with a nominal interest rate of 12%, and interest paid monthly. a) What is the monthly loan payment? b) What is the loan's EAR (Effective Annual Rate)?

a) To calculate the monthly loan payment of an amortizing loan, we can use the formula for a fixed installment loan which is derived from the annuity formula:

\[ P = \frac{L \times i}{1 - (1 + i)^{-n}} \]

Where: - P is the monthly payment - L is the loan amount ($15,000 in this case) - i is the monthly interest rate (annual nominal rate divided by 12) - n is the total number of payments (5 years x 12 months per year)

First, we'll calculate the monthly interest rate: The nominal interest rate is 12%, so \[ i = \frac{12\%}{12} = 1\% \text { or } 0.01 \text { per month} \]

Next, we'll calculate the number of payments: \[ n = 5 \text{ years} \times 12 \text{ months/year} = 60 \text{ payments} \]

Now, we can calculate the monthly payment (P): \[ P = \frac{$15,000 \times 0.01}{1 - (1 + 0.01)^{-60}} \] \[ P = \frac{150}{1 - (1.01)^{-60}} \] \[ P = \frac{150}{1 - (1.01)^{-60}} \] \[ P = \frac{150}{1 - 0.54792} \] \[ P = \frac{150}{0.45208} \] \[ P \approx 331.67 \]

So, the monthly payment would be approximately $331.67.

b) The Effective Annual Rate (EAR) can be calculated using the formula:

\[ (1 + i)^n - 1 \]

Where: - i is the monthly interest rate (which we've calculated as 0.01) - n is the number of periods in a year (which is 12 for monthly payments)

\[ EAR = (1 + 0.01)^{12} - 1 \] \[ EAR = (1.01)^{12} - 1 \] \[ EAR \approx 1.126825 - 1 \] \[ EAR \approx 0.126825 \text{ or } 12.6825\% \]

The loan's EAR is approximately 12.6825%.