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Sagot :
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 = [tex]\frac{1}{r} - \frac{1}{r}. \frac{1}{(1+r)^{t} }[/tex]
and t = 3 years = 36 months
Now,
As we know,
Monthly loan payment = [tex]\frac{Loan amount}{Annuity factor}[/tex]
⇒$526.83 = 14,000( 1 + r)¹² / [tex]\frac{1}{r} - \frac{1}{r}. \frac{1}{(1+r)^{t} }[/tex]
By solving we get
r = 1.019%
Now,
Nominal interest rate = 1.019%×12 = 12.23%
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