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%