Question

Amortization schedule with periodic payments. Moulton Motors is advertising the following deal on a used Honda​ Accord: ​ "Monthly payments of $165.73 for the next 60 months and this beauty can be​ yours!" The sticker price of the car is $7,800. 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?

________% ​(Round to five decimal​ places.)

20 parts remaining

Answer 1

We are given the following information:

Monthly Payment	PMT	165.73
Rate of interest	r	To be calculated
Number of years	n	5.00 years of 5 x 12 = 60 payments
Monthly	frequency	12.00
Loan amount	PV	7800.00

We need to solve the following equation to arrive at the required r

• Rate function calculates only the periodic rate. As the frequency is monthly so it needs to be multiplied by 12 to get the annual rate.
• PMT is an outflow so it is negative. Loan when taken is an inflow so it is positive

Therefore APR or r is 10%

Effective annual rate is as follows:

Amortization schedule:

Month	Opening Balance	Interest	Principal repayment	Closing Balance
1	$              7,800.00	$               65.01	$                         100.72	$           7,699.28
2	$              7,699.28	$               64.17	$                         101.56	$           7,597.71
3	$              7,597.71	$               63.32	$                         102.41	$           7,495.30
4	$              7,495.30	$               62.47	$                         103.26	$           7,392.04
5	$              7,392.04	$               61.61	$                         104.12	$           7,287.91
6	$              7,287.91	$               60.74	$                         104.99	$           7,182.92

Opening balance = previous year's closing balance
Closing balance = Opening balance-Principal repayment
PMT is calculated as per the above formula
Interest = 0.10/12 x opening balance
Principal repayment = PMT - Interest

Monthly interest rate is 10/12 = 0.83%