Expert: Sherman D. - 11/16/2004

Question
1) if $1000 is invested at 8% per year, in about how many years will the investment be worth $2000?
2) suppose that $1000 is invested at 8% annual interest compounded monthly.
 a)find the value of the investment after 1 year.
 b)find the effective annual yield.

Answer
If you are talking about compound interest for both.

A = P(1 + r)^(t)

1.)
2000 = 1000(1 + .08)^t
2000 = 1000(1.08)^t
1.08^t = 2
log(1.08)2 = t
t = (log 2)/(log 1.08)
t = about 9 years

2.)
A = P(1 + (r/n))^(nt)
A = 1000(1 + (.08/12))^(12t)
A = 1000(1 + (1/150))^(12 * 12)
A = 1000(1 + (1/150))^(144)
A = 1000(2.60338924...)
A = $2603.39

each month compounded and there are 12 months in a year. so that is how i got the 12 * 12.

according to a site i found, the EAY is found like this
Y = (1 + (r/m))^M - 1
or
Y = (1 + (r/n))^(nt) - 1
Doing this, i get
EAY = 1.60338924...
or i am assuming thats about
EAY = 1.6%
not certain how it is to be written, so i can't remember doing EAY.

Info found at http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/calctopic1/logs.html
and
http://cs.selu.edu/~rbyrd/math/regular/