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 $576.83 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?
enter percentages rounded to 4 decimal places %
b. What effective interest rate are they paying?
enter percentages rounded to 4 decimal places %

Round your answer to 4 decimal places for a and b. The tolerance is ± 0.0005.

c. How much of the 14th month’s payment is interest? How much is principal?
payment interest = $enter a dollar amount rounded to the nearest whole  , and principal = $enter a dollar amount rounded to the nearest whole
d. How much of the 18th month’s payment is interest? How much is principal?
payment interest = $enter a dollar amount rounded to the nearest whole  , and principal = $enter a dollar amount rounded to the nearest whole
e. How much of the 22nd month’s payment is interest? How much is principal?
payment interest = $enter a dollar amount rounded to the nearest whole  , and principal = $enter a dollar amount rounded to the nearest whole

can you please solve it in excel , thanks

Answer 1

future value = Present value*(1+(r/n))^n

where r = nominal rate

n = number of periods

let (r/n) = i

Truck value = 15000

Down payment = 1000

loan value = 15000 - 1000 = 14000

so amount after one year = 14000*(1+i)^12

Present value of annuity = P*[1 - (1+i)^-n / i ]

P = monthly payments = 576.83

i = monthly interest rate

n = number of periods = 36

amount after one year should equal to present value of annuity

so,

14000*(1+i)^12 = 576.83*(1 - (1+i)^-36 / i)

now we have to calculate 'i' using trail and error method

solving for i we get monthly rate = 1.3323%

a)

so nominal rate = 1.3427%*12 = 15.9879%

b)

effective rate = (1+1.3427%)^12 - 1 = 17.2131%

c,d,e)

Formulas will be as follows: