SOLUTION: You invest $ 27,000 for a period of 14 years and rely on an investment value of $ 100,000. With which monthly compound annual compound interest rate (12 times per year). You may ge

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: You invest $ 27,000 for a period of 14 years and rely on an investment value of $ 100,000. With which monthly compound annual compound interest rate (12 times per year). You may ge      Log On


   

Question 1091449: You invest $ 27,000 for a period of 14 years and rely on an investment value of $ 100,000. With which monthly compound annual compound interest rate (12 times per year). You may get this amount at the end of the placement.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You invest $ 27,000 for a period of 14 years and rely on an investment value of $ 100,000.
With which monthly compound annual compound interest rate (12 times per year). You may get this amount at the end of the placement.
:
Using the formula A+=+Ao%281%2B%28r%2Fn%29%29%5E%28nt%29 where:
A = final amt
Ao = Initial amt
r = interest rate in decimal form
n = number of times interest is compound per year
t = time in years
in this problem we know:
A = 100000
Ao = 27000
r is unknown
n = 12
t = 14 yrs
:
27000%281%2B%28r%2F12%29%29%5E%28%2812%2A14%29%29%29+=+100000
%281%2B%28r%2F12%29%29%5E168+=+100000%2F27000
%281%2B%28r%2F12%29%29%5E168+=+3.7037
using natural logs, use the log equiv of the exponent
168ln%281%2B%28r%2F12%29%29+=+ln%28100000%2F27000%29
find the ln
168ln%281%2B%28r%2F12%29%29+=+1.309
divide both sides by 168
ln%281%2B%28r%2F12%29%29+=+1.309%2F168
ln%281%2B%28r%2F12%29%29+=+.0779365
Find the anti-ln of both sides
1 + r%2F12 = 1.0078241
subtract 1 from both sides
r%2F12 = .0078241
multiply both sides by 12
r = .0934 or 9.34% interest rate required
:
A lot of math here; you better check my work. CK