Question

You have just taken out a $ 22,000 car loan with a 4 % ​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.)

1. When you make your first payment, how much money will go toward the principle of the loan? (Round to the nearest cent)

2. When you make your first payment, how much money will go toward the interest? (Round to the nearest cent)

Answer 1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

22000= Cash Flow*((1-(1+ 4/1200)^(-5*12))/(4/1200))

Cash Flow = 405.16

	Monthly rate(M)=	yearly rate/12=	0.33%	Monthly payment=	405.16
Month	Beginning balance (A)	Monthly payment	Interest = M*A	Principal paid	Ending balance
1	22000.00	405.16	73.33	331.83	21668.17

1

331.83

2

73.33

Where

Interest paid = Beginning balance * Monthly interest rate

Principal = Monthly payment – interest paid