Question

Amortization schedule with periodic payments. Moulton Motors is advertising the following deal on a used Honda Accord: "Monthly payments of $178.29 for the next 60 months and this beauty can be yours!" The sticker price of the car is $8,200. If you bought the car, what interest rate would you be paying in both APR and EAR terms? What is the amortization schedule of the first six payments? If you bought the car, what monthly interest rate would you be paying?

Please can i get help solve this entire problem?

Answer 1

if we bought the car we would be paying an interest rate of 11.04%, please find the calculation below

Particulars	Amount
Present value	8200
Monthly Payment	-178.26
No of installments	60
Future Value/Maturity Value	0.00
Interest rate	0.92%

0.92*12 = 11.04% As we have taken the values of payments and no of installments on monthly basis we have received the interest rate on monthly basis. To make it a yearly number we need to multiply it by 12 and get 11.04%

APR = 11.04

EAR = (1 + (APR/no of months))^{no of months} - 1

= (1 + (11.04/12))^{12 - 1}

^{= 11.61%}

^{Amortization schedule for the first six months}

Month	Principal	Interest Rate	Interest Amount	EMI	Balance principal
1	8200.00	0.920%	75.44	178.26	8097.2
2	8097.18	0.920%	74.49	178.26	7993.4
3	7993.41	0.920%	73.54	178.26	7888.7
4	7888.69	0.920%	72.58	178.26	7783.0
5	7783.01	0.920%	71.60	178.26	7676.4
6	7676.35	0.920%	70.62	178.26	7568.7
7	7568.72	0.920%	69.63	178.26	7460.1
8	7460.09	0.920%	68.63	178.26	7350.5
9	7350.46	0.920%	67.62	178.26	7239.8
10	7239.82	0.920%	66.61	178.26	7128.2