You have just taken out a $ 17 comma 000 car loan with a 6 %...

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.)

Expert Solution

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

jeff jeffy answered 10 months ago

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