Question

You purchase a car for 10,000

The car loan is financed with a 5% per year, 5 year loan with annyual payments starting at time 1 (1 year from today) through time 5

Each payment reduces the principal by a certain amount until the loan is completely paid off.

What is the interest component of the first payment?

(I am allowed to use the TI-34 and BAII Plus calculators)

Answer 1

Step-1:Calculation of annual payment
	Annual Payment		=	Loan Amount / Present Value of annuity of 1
			=	$ 10,000.00	/	4.3295
			=	$   2,309.75
	Working:
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.05)^-5)/0.05			i	5%
				=	4.3295			n	5
Step-2:Amortization of Loan amount
	Year	Beginning Loan Amount			Interest expense for the Year				Annual Payment		Reduction of Loan Principal			Ending Loan Amount
	1		$ 10,000.00			$ 500.00			$ 2,309.75			$ 1,809.75			$ 8,190.25
	2		$   8,190.25			$ 409.51			$ 2,309.75			$ 1,900.24			$ 6,290.02
	3		$   6,290.02			$ 314.50			$ 2,309.75			$ 1,995.25			$ 4,294.77
	4		$   4,294.77			$ 214.74			$ 2,309.75			$ 2,095.01			$ 2,199.76
	5		$   2,199.76			$ 109.99			$ 2,309.75			$ 2,199.76			0
Thus,
Interest component of the first payment				$ 500.00