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 $526.83 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

Answer 1

Answer:

Nominal interest rate =  12.23%

Explanation:

Given - 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 $526.83 at the end of each month over years 2, 3, and

             4 (first payment is in 13th month).

To find - a. What nominal interest rate is Aerotron paying on the loan.

Proof -

As given ,

Price - $15,000

Down Payment - $1,000

⇒Loan Payment = $15,000 - $1,000

As given,

He will not pay for the entire first year. After that he will pay $526.83 for next 3 years.

Now,

Interest rate for 1 month = r %

So,

Loan after 1 year = 14,000( 1 + r)¹²

And

Annuity factor = $\frac{1}{r} - \frac{1}{r}. \frac{1}{(1+r)^{t} }$

and t = 3 years = 36 months

Now,

As we know,

Monthly loan payment = $\frac{Loan amount}{Annuity factor}$

⇒$526.83 = 14,000( 1 + r)¹² / $\frac{1}{r} - \frac{1}{r}. \frac{1}{(1+r)^{t} }$

By solving we get

r = 1.019%

Now,

Nominal interest rate = 1.019%×12 = 12.23%