Question 1011179


A pottery factory purchases a continuous belt conveyor kiln for $50,000. A 6.5% APR loan with monthly payments is taken out to purchase the kiln. If the monthly payments are $501, over what term is this loan being paid?

Select one:
1. 10 years
2. 11 years
3. 12 years
4. 13 years
Next
<pre>Formula to use: periods, or {{{M = (P(r/12)(1 + r/12)^n)/((1 + r/12)^n - 1)}}} 
{{{501 = (50000(.065/12)(1 + .065/12)^n)/((1 + .065/12)^n - 1)}}} ------- Substituting 501 for M (end-of-month payment), 50,000 for P, and .065 for r
{{{501 = (50000(.005417)(1 + .005417)^n)/((1 + .005417)^n - 1)}}}
{{{501 = (270.83333(1.005417)^n)/((1.005417)^n - 1)}}}
{{{270.83333(1.005417)^n = 501((1.005417)^n - 1)}}} --------- Cross-multiplying 
{{{270.83333(1.005417)^n = 501(1.005417)^n - 501}}}
{{{270.83333(1.005417)^n - 501(1.005417)^n = - 501}}}
{{{- 230.16667(1.005417)^n = - 501}}}
{{{(1.005417)^n = (- 501)/(- 230.16667)}}} -------- Dividing by – 230.16667 
{{{n = log (1.005417, ((- 501)/(- 230.16667)))}}} ---- Converting to LOGARITHMIC form
{{{n = log (((- 501)/(- 230.16667)))/log ((1.005417))}}} ------------- Applying change of base
n, or number of months/periods = 143.9828 

Number of years = {{{143.9828/12}}}, or 11.99857 &#8776; {{{highlight_green(12)}}} (CHOICE 3)