Question

You have just taken out an $18,000 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?

QUESTION

When you make your first​ payment, ​$????? will go toward the principal of the loan and ​$???? will go toward the interest

Answer 1

When you make your first​ payment, ​$257.99 will go toward the principal of the loan and ​$90.00 will go toward the interest.

Working:

Step-1:Calculation of monthly payment
Loan is the present value of monthly payments.
Monthly Payment	=	Loan amount	/	Present value of annuity of 1
	=	$ 18,000.00	/	51.72556
	=	$       347.99
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
	=	51.7255608		n	=	5*12	=	60
Step-2:Calculation of payment towards principal and interest
Total Payment		$       347.99
Less payment towards interest		$         90.00
Payment towards interest		$       257.99
Working:
Interest for the first month	=	Beginning Loan	*	Monthly Interest rate
	=	$ 18,000.00	*	0.005
	=	$         90.00