Question

1. Nicole Franco buys a Jeep Wrangler for $31,445, paying 20% down or $6,289 in cash and obtaining an auto loan for the balance. If the loan is to be repaid in equal annual installments at the end of each of 5 years at an interest rate of 4.75%,
   1. What is the amount of each annual payment?
   2. Create an amortization table?

Answer 1

Loan = amount*(1-down%) = 31445-6289=25156

a

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

C = Cash flow per period

i = interest rate

n = number of payments

25156= Cash Flow*((1-(1+ 4.75/100)^-5)/(4.75/100))

Cash Flow = 5770.31

b

	Annual rate(M)=	yearly rate/1=	4.75%	Annual payment=	5770.31
Year	Beginning balance (A)	Annual payment	Interest = M*A	Principal paid	Ending balance
1	25156.00	5770.31	1194.91	4575.40	20580.60
2	20580.60	5770.31	977.58	4792.73	15787.88
3	15787.88	5770.31	749.92	5020.38	10767.50
4	10767.50	5770.31	511.46	5258.85	5508.65
5	5508.65	5770.31	261.66	5508.65	0.00

Where

Interest paid = Beginning balance * Annual interest rate

Principal = Annual payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Year ending balance