You have been investing $165 a month for the last 12 years. today, your investment account is worth $60,508.29. what is your average rate of return on your investments? 13.77 percent 13.80 percent 13.84 percent 13.89 percent 14.03 percent

Given:
Future value, F=60508.29
Monthly payment, A = 165
Compounding period = month
Number of periods, n = 12*12=144
interest per period = i   [ to be found ]

We have the relationship
F=A((1+i)^n-1)/i
but there is no explicit formula for i for given F, A and n.
We need to solve a non-linear equation for the value of i, the monthly interest rate.
One of the ways is to solve it by fixed iteration, i.e. 
1. using the given relation, express i in terms of other parameters.
2. select an initial value of i
3. evaluate i according the equation in step 1 until the value is stable.

Here we will use the relationship to express
i=((60508.29*i)/165+1)^(1/144)-1  [ notice that i is on both sides of = sign ]
using an initial value of i=0.01 (about 1% per month).
Successively, we get
i=((60508.29*0.01)/165+1)^(1/144)-1=0.01075571
i=((60508.29*0.01075571)/165+1)^(1/144)-1=0.011160681, similarly
i=0.0113685
i=0.0114728
i=0.0115246
i=0.0115502
i=0.0115628
i=0.0115690
i=0.0115720
Assuming the above has stablilized, and the APR is 12 time the above value, namely
Annual percentage rate = 0.01157205998210142*12=0.13886=13.89%

Z-gadgets has developed a mini-laptop that will be marketed in developing countries. it is estimated that the requirement for the new product will start out slow and accelerate as the product becomes increasingly familiar to worldwide consumers. to begin to staff the new production facilities, the company should conduct a(n):   demand forecast

4.94.. let me know if i'm correct