Question

- you want to buy a brand-new car. Its price is $49,000 and the dealer’s special financing offers you 2.75% APR. What will be your monthly payment if you want to pay the car loan off in 6 years?

How much interest money will you save if you make more payments and pay the loan off in 3 years?

Answer 1

1)	Monthly Payment	=	Loan amount	/	Present value of annuity of 1
		=	$ 49,000.00	/	66.3038053
		=	$       739.02
	Working:
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.002292)^-72)/0.002292		i	=	2.75%/12	=	0.002292
		=	66.3038053		n	=	6*12	=	72
2)	Interest saved		$   2,104.48
Working:
# 1	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.002292)^-36)/0.002292		i	=	2.75%/12	=	0.002292
		=	34.5170816		n	=	3*12	=	36
# 2	Monthly Payment	=	Loan amount	/	Present value of annuity of 1
		=	$ 49,000.00	/	34.5170816
		=	$   1,419.59
# 3			6 Years		3 Years		Difference
	Monthly Payment		$       739.02		$   1,419.59
	Months		72		36
	Total repayments		$ 53,209.62		$ 51,105.13
	Loan		$ 49,000.00		$ 49,000.00
	Interest		$   4,209.62		$   2,105.13		$ 2,104.48