Question

Aerotron Electronics has just bought a used delivery truck for $15,000. The small business paid $1,000 down and financed the rest, with the agreement to pay nothing for the entire first year and then to pay $556.83 at the end of each month over years 2, 3, and 4 (first payment is in 13th month).

a. What nominal interest rate is Aerotron paying on the loan?

b. What effective interest rate are they paying?

c. How much of the 14th month’s payment is interest? How much is principal?

d.  How much of the 18th month’s payment is interest? How much is principal?

e.  How much of the 22nd month’s payment is interest? How much is principal?

Answer 1

1) The nominal interest rate is Aerotron paying on the loan.

Price of truck = $ 15,000 Down payment = $ 1,000 Borrowed amount = $ 14,000 Monthly payment = $ 506.83 Payment starts from 13th month onwards. Number of payment = 3 12 = 36 months

According to the information given in the question

              where A 36 is annuity function

The nominal interest rate is 10.63 % compounded monthly

b) The effective interest rate are they paying

Let i be the effective annual rate of interest. Therefore

the effective annual rate of interest is 11.16 %

c) The 14th month’s payment is interest & principal

Loan outstanding after 13th month = 506.83 X a35 = 506.83 X 29.98 = 15195.27

The interest paid in the 14th payment is 15195.57 X (0.1063/12) =134.607$

principal amount 372$

d)18th month’s payment is interest

506.83*27.98=14181.1

=14181.1*0.1063/12

=125$

386$ principal amount

e)  22nd month’s payment is interest 107$

principal 400$