Question

Purchase Price	$33,500.00			Finance Rate Table
less				Term	No Rebate	Rebate
Down Payment	$3,500.00			1	12.50%	19.70%
Trade-in Value	$4,500.00			2	14.90%	20.90%
Rebate	$1,000.00			3	17.30%	22.10%
				4	18.50%	23.30%
Loan Amount	$24,500.00			5	19.70%	24.50%
	--------------------Term of Loan-----------------------
	1	2	3	4	5
Finance Rate	19.70%	20.90%	22.10%	23.30%	24.50%
Monthly Payment	$2,266.03	$1,257.75	$936.93	$789.29	$711.94
Total Payment	$27,192.35	$30,185.89	$33,729.63	$37,886.09	$42,716.61
Finance Charge	$2,692.35	$5,685.89	$9,229.63	$13,386.09	$18,216.61

Please answer the following below using your Automobile Loan Calculator workbook along with the following information:

• Purchase Price is $33,500
• Down Payment is $3,500
• Trade-in Value is $4,500
• Customers get $1,000 if they elect to take the Rebate
• Use the Finance Rate Table provided below:

• Term	No Rebate	Rebate
  1	12.5%	19.7%
  2	14.9%	20.9%
  3	17.3%	22.1%
  4	18.5%	23.3%
  5	19.7%	24.5%

A) If a customer elects to take the Rebate, what is the Loan Amount?

B) If a customer does not elect to take the rebate, what would the monthly payment be for a 3-year loan?

C) If a customer elects to take the $1,000 Rebate, what would be the Total Payments for a 5-year loan?

D) What is the difference in Monthly Payment amounts for customers who do and do not elect to take the Rebate for a 1-year loan?

E) What is the difference in Finance Charges for customers who do and do not elect to take the Rebate for a 1-year loan?

Answer 1

Answer a

Loan amount With Rebate is (33500-3500-4500-1000)=$24500

Answer b

Without Rebate Loan Amount is 24500+1000=$25500

Interest Rate for a 3 year Loan =17.3%

Monthly Rate= 17.3/12=1.44%

Period = 3*12=36 months

Hence, PV = A*(1-(1+r)^-n)/r

or, 25500=A*(1-(1+1.44%)^-36)/1.44%

or, 25500=A*(1-(1.0144)^-36)/0.0144

or, 25500=A*(1-0.5977)/0.0144

or, 25500=A*0.4023/0.0144

or, A =25500*0.0144/0.4023

or, A =$912.70

Hence Monthly Payment will be $912.7

Answer c

Loan Amount with Rebate = $24500

Interest Rate = 24.5%

Monthly Rate = 2.04%

Period =5*12=60 months

Hence, PV = A*(1-(1+r)^-n)/r

or, 24500=A*(1-(1+2.04%)^-60)/2.04%

or, 24500=A*(1-(1.0204)^-60)/0.0204

or, 24500=A*(1-0.2977)/0.0204

or, 24500=A*0.7023/0.0144

or, A =24500*0.0204/0.7023

or, A =$711.66

Hence Monthly Payment will be $711.66

Total Payment for 5 year = 711.66*60=$42699.46

Answer d

Without Rebate Loan Amount is $25500

Interest Rate for a 1 year Loan =12.5%

Monthly Rate= 12.5/12=1.04%

Period = 1*12=12 months

Hence, PV = A*(1-(1+r)^-n)/r

or, 25500=A*(1-(1+1.04%)^-12)/1.04%

or, 25500=A*(1-(1.0104)^-12)/0.0104

or, 25500=A*(1-0.8832)/0.0104

or, 25500=A*0.1168/0.0104

or, A =25500*0.0104/0.1168

or, A =$2271.37

Hence Monthly Payment will be $2271.37

With Rebate Loan Amount is $24500

Interest Rate for a 1 year Loan =19.7%

Monthly Rate= 19.7/12=1.64%

Period = 1*12=12 months

Hence, PV = A*(1-(1+r)^-n)/r

or, 24500=A*(1-(1+1.64%)^-12)/1.64%

or, 24500=A*(1-(1.0164)^-12)/0.0164

or, 24500=A*(1-0.8227)/0.0164

or, 24500=A*0.1773/0.0164

or, A =24500*0.0164/0.1773

or, A =$2265.79

Hence Monthly Payment will be $2265.79

Hence difference is 2265.79-2271.37=-$5.58

ANswer e

Total PAyment without Rebate = 2271.37*12 = $27256.44

Hence Finance Charge =  27256.44-25500 = $1756.44

Total PAyment with Rebate = 2265.79*12 = $27189.48

Hence Finance Charge =  27189.48-24500 = $2689.48

Hence difference is 2689.48-1756.44=$933.04