Question

You want to buy a car, and a local bank will lend you $25,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 10% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places.

Answer 1

Answer:

Monthy payment will be of $536.99. The loan's EAR is 8.72%.

Explanation:

To solve this exercise, you first has to convert the nominal rate to real rate with this formula: i=(1+r/m)^m−1

i=(1+0.1/12)^12−1

i=0.104713

I=i×100=10.4713%

To calculate the loan monthly payment, you need to calcualte the monthy rate (10.41/12)=8.72

With this, yu calculate the discount factor D, using the number of periodic payments (60) and the rate:  

D=((1+r)^n-1)/(r*[(1+r)^n]

D=(((1+0.008726)^60)-1)/(0.008726*(1+0.008726)^60)=46.56

Finally, yo calculate the loan payment by: A/D=25,000/46.56=536.99