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 $ 506.83 at the end of each month over years 2, 3, and 4 (first payment is in thirteenth 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 fourteenth month's payment is interest? How much is principal? payment interest = $ , and principal = $
d. How much of the eighteenth month's payment is interest? How much is principal? payment interest = $ , and principal = $
e. How much of the twenty-second month's payment is interest? How much is principal? payment interest = $ , and principal= $

Answer 1

Answer:

a) 12.23%

b)  12.94%

c) 14th month payment interest = $157.33

   14th month principal =  $369.50

d)  18th month payment interest = $142.04

    18th month payment interest = $384.79

e) 22nd month payment interest = $126.12

   22nd month payment interest = $400.71

Explanation:

price of truck = $15000

down payment = $1000

Loan amount = $14,000

assume monthly interest rate = r%

Loan amount after 1 year will be = 14000 * (1+r%)12

next we will determine the annuity factor = [  (1/r)-[(1/r)*(1/ (1+r)t)] ]

r = periodic interest rate , t = number of payments

monthly loan payment = $14000*(1+r%)12 / [  (1/r)-[(1/r)*(1/ (1+r)36)] ]

hence r = 1.019%

a) nominal interest rate

=  1.019% *12 = 12.23%

b) effective interest rate

= (1+1.019%)^12 -1 = 12.94%

attached below is the Amortization schedule

c) 14th month payment interest = $157.33

    14th month principal =  $369.50

d) 18th month payment interest = $142.04

    18th month payment interest = $384.79

e) 22nd month payment interest = $126.12

   22nd month payment interest = $400.71