Question

The owner of a automobile repair center purchased new electronic diagnostic equipment for $12000. He paid 10 precent down and then paid 60 precent monthly of $203.81. Determine the APR of the loan to the nearest one half of a precent

Answer 1

The owner of a automobile repair center purchased new electronic diagnostic equipment for $12000. He paid 10 pERcent down and then paid 60 pAYMENTS monthly of $203.81.

Net loan, P=12000*0.9=10800 
Monthly payment, A=203.81
Number of payments, n=60

Let i=APR

A=P(i/12*(1+i/12)^n)/((1+i/12)^n-1)
Substituting values
203.81=10800(i/12*(1+i/12)^60)/((1+i/12)^n-1)

=>
12*203.81/10800=i(1+i/12)^60/((1+i/12)^60-1)

To solve for i, we form the iterative equation:
(1+i/12)^60=(12*203.81/10800)/i*((1+i/12)^60-1)
i=12*(12*203.81/10800*((1+i/12)^60-1)/i)^(1/60-1)
try i=0.05, 
f(0.05)=0.05
Therefore the APR is 5%