Find the interest rate needed for an investment of $5000 to grow to an amount of $9000 in 4 yr?

Question

if interest is compounded continuously.

Answer 1

Since the interest is compounded continuously, you need to use the formula P_0 * e^(rt) = P, where r is the growth rate (which is not actually the interest rate). I'm assuming that you have some experience with exponential growth, so this equation should look familiar to you.

In this case, P = 9000, P_0 = 4000, and t = 4, so the equation is:

e^(4r) = 1.8.

Take ln of both sides (you'll need a calculator for the right hand side):

4r = .588,
so r = .147.

Now, to find the annual interest rate, you need to put this value of r back into the original equation, and set t=1. This will tell you how much your money grows in one year. You get:

P/P_0 = e^(.147) = 1.158, so the interest rate is 15.8%.

Answer 2

Growth factor = $9000/$5000 = 1.80
Compound annual growth rate = growth factor to the power of 1/n
where n = investment period
Compound annual growth rate = (1.80^0.25)-1 = 15.8%
... no comment on tax ;-)