If I invest $2,000 on 1/1/01 and it returns $10,000 on 1/1/06, what is the rate of return?

Question

anonymous · Answer

You could use the future value formula:
$$FV =P(1+r)^{Y}$$
Where FV is the future value of your money ($10,000), P is the principle, or initial amount of money ($2,000), r is the annual rate of return (which we're trying to solve for), and Y is the number of years the money is let to grow (2006-2001 = 5 years).

So when you plug in these numbers the equation looks like this:
$$10,000=2,000(1+r)^{5}$$
And then solve for r:
$$[10,000=2,000(1+r)^{5}]/2,000\rightarrow5=(1+r)^{5}$$
$$\sqrt[5]{5}=\sqrt[5]{(1+r)^{5}}\rightarrow1.379723=1+r$$
$$1.37973-1=1+r-1\rightarrow r=0.37973=37.973percent$$
So your annual rate of return is 37.973 %.

anonymous · Answer

Jpomer35 - that makes sense to me.  Thanks so much for your help!