Question

Question 1: You are buying a new $40,000 car. You must put down 10% and then finance the remainder for 5 years @ 8%. What is your monthly payment?

A. $811.06

B. $849.88

C. $729.95

D. $770.50

Question 2: Refer to the previous question. If you wanted to pay off the car immediately after you made the 43rd payment, how much would you have to pay the finance company?

A. $6,868.50
B. $11,695.02
C. $9,767.42
D. Insufficient information to determine

Answer 1

question 1:

C.$729.95

monthly payment = r * loan amount / [1-(1+r)^(-n)]

here,

r= 8% per year =>8%*1/12 per month

=>0.6667%

=>0.006667.

loan amount= 40,000*(1-0.10 down payment)

=>$36,000

n= 5 years *12

=>60.

monthly payment = (0.006667*36,000) / [1-(1.006667)^(-60)]

=>240.12/0.3288029

=>$730.28......... (closer to $729.95.....minute differences arise due to rounding off of present value factors).

question 2:

B.$11,695.02.

the amount to be paid off after 43rd payment

=> monthly payment * PV of annuity factor

PV of annuity factor = [1-(1+r)^(-n)]/r

here,

r= 0.00667.

n=17 months remaining

amount to be paid = 729.95 * [1-(1.00667)^(-17)]/0.00667

=>729.95*16.0211994

=>$11,694.67....(close to 11,695.02...minute difference due to rounding off of present value factors).