SOLUTION: I have a $9000 loan at 5% interest. What monthly payment will let you pay off the loan in each amount of time? a.) 36 months b.) 39 months c.) 48 months I'm taking an Algebra fo

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Question 856820: I have a $9000 loan at 5% interest. What monthly payment will let you pay off the loan in each amount of time? a.) 36 months b.) 39 months c.) 48 months
I'm taking an Algebra for Teachers college course and am confused with how to arrive at the solution of $269.74. What is an easy way to explain this to high school students? Thanks!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I have a $9000 loan at 5% interest.
What monthly payment will let you pay off the loan in each amount of time?
a.) 36 months b.) 39 months c.) 48 months
:
It's pretty cumbersome equation, I don't pretend to understand it.
MP = where:
Mp = monthly payment
p = amt borrowed
r = interest rate/100
n = period per year
t = no. of yrs
IN this problem we will try to find nt
= 269.74
do the math
%2837.5%28%281.004167%29%5E%28nt%29%29%29%2F%28%281.004167%29%5E%28nt%29-1%29 = 269.74
:
%28%281.004167%29%5E%28nt%29%29%2F%28%281.004167%29%5E%28nt%29-1%29 = 269.74%2F37.5
:
%28%281.004167%29%5E%28nt%29%29%2F%28%281.004167%29%5E%28nt%29-1%29 = 7.193
1.004167)^nt = 7.193(1.004167^nt - 1)
:
1.004167)^nt = 7.193(1.004167)^nt - 7.193
:
7.193 = 7.193(1.004167)^nt - 1(1.004167^nt)
:
7.193 = 6.193(1.004167)^nt
7.193%2F6.193 = 1.004167^nt
1.161467 = 1.004167^nt
nt = log%281.161467%29%2Flog%281.004167%29
:
nt = 35.996 ~ 36 months
:
I checked this using the financial feature on the Ti83 (took about 20 seconds)
If you can keep your students attention thru this, you are a genius!!