Question

You want to buy a new sports coupe for $74,400, and the finance office at the dealership has quoted you a loan with an apr of 6.8 percent for 48 months to buy the car. what will your monthly payments be? (do not round intermediate calculations and round your answer to 2 decimal places,
e.g., 32.16.) monthly payment $ what is the effective annual rate on this loan? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,
e.g., 32.16.) effective annual rate %

Answer 1

Monthly payment = $1774.71 
Effective annual rate = 7.02% 
 The equation for a loan payment is
 P = r(PV)/(1-(1+r)^(-n))
 where
 P = Payment per period
 PV = Present value
 r = interest rate per period
 n = number of periods 
 Since the 6.8% interest rate is APR, we need to divide by 12 to get the interest per month. So in the above equation r = 0.068/12 = 0.005666667, the number of periods is 48 and the Present Value is 74400. Let's plug in the numbers and calculate.
 P = r(PV)/(1-(1+r)^(-n))
 P = 0.00566666666666667(74400)/(1-(1+0.00566666666666667)^(-48))
 P = 421.6/(1-(1.00566666666666667)^(-48))
 P = 421.6/(1-0.762439412691304)
 P = 421.6/0.237560587308696
 P = 1774.70516
 So the month payment rounded to 2 decimal places is $1774.71 
 The effective interest rate is
 ER = (1 + r/12)^12 - 1 
 Let's plug in the numbers and calculate.
 ER = (1 + 0.068/12)^12 - 1
 ER = (1 + 0.00566666666666667)^12 - 1
 ER = (1.00566666666666667)^12 - 1
 ER = 1.07015988024972 - 1
 ER = 0.07015988024972 = 7.015988024972% 
 So after rounding, the effective interest rate is 7.02%