Question

You want to buy a car, and a local bank will lend you $20,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 10% with interest paid monthly.
1. What will be the monthly loan payment?

2. What will be the loan's EAR?

Answer 1

Amortizing a loan P over n periods at i% interest / period, the payment per period is given by:
$A= P(i(1+i)^n)/((1+i)^n-1)$

In given situation,
P=20000
period=month
i=10%/12
n=5*12=60 months

A.  monthly payment amount
$A= P(i(1+i)^n)/((1+i)^n-1)$
$= 20000(.1/12(1+.1/12)^60)/((1+.1/12)^60-1)$
$=424.98$ to the nearest cent

B. EAR (effective annual rate)
the APR is 10%, but compounded monthly.
So 
EAR=(1+i/12)^12-1
=(1+0.1/12)^12-1
=0.104713
=10.4713%  (effective annual rate)