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 $546.83 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 the loan? (please try to show me with goal seek and Excel)

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

a. Let i12 be the nominal interest rate compounded monthly.

According to the information given in the question,

14000=506.83×(1+ i12 )−12×a36

where a36 is annuity function.

=>14000=506.83×(1+i¹²/12)^-12  * (1-(1+i¹²/12)^-36/i¹²/12)

Thus, the nominal interest rate is 10.63% compounded monthly.

b. Let i be the effective annual rate of interest. Therefore

(1+i12/12)¹²=1+i

=>i=0.1116

Thus, the effective annual rate of interest is 11.16 %

c. 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) = 134.6

Principal paid = 506.83 - 134.6 = 372.23

d. Loan outstanding after 17th month = 506.83 X a31 = 506.83 X 27.004 = 13686.46

The interest paid in the 14th payment is 13686.46 X (0.1063/12) = 124.24

Principal paid = 506.83 - 121.24 = 385.59

e. Loan outstanding after 21st month = 506.83 X a27 = 506.83 X 23.92 = 12123.49

The interest paid in the 14th payment is 12123.49 X (0.1063/12) = 107.39

Principal paid = 506.83 - 107.39 = 399.44