Question

You have just taken out a $ 17 comma 000 car loan with a 6 % ​APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest?  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

Step-1:Calculation of monthly payment
Monthly Payment	=	Loan amount / Present value of annuity of 1
	=	$       17,000	/	51.725561
	=	$       328.66
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i			Where,
	=	(1-(1+0.005)^-60)/0.005			i	6%/12	=	0.005
	=	51.725561			n	5*12	=	60
Step-2:Calculation of principal and interest in first month's payment
First month's interest	=	Loan amount * Monthly Interest rate
	=	$       17,000	*	0.005
	=	$               85
First month's principal repayment	=	$       328.66	-	$           85
	=	$       243.66