"Doubling your money.." problem!?

Question

There are three of these questions with different times of how often it is compounded (annually, quarterly, etc.) and I would like to know how to do one so I can do the rest.

"Determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25% compounded annually."

Please be detailed! I'm trying to understand my homework.

P.S., what equation would I use for the same problem if it was for compounded continuously?

P=Ae^rt

I

Answer 1

F = P(1+i)^t

or

2P = P(1+i)^t

P is the present value, 2P is the future value representing a quantity two times the present value.  i is the interest rate, t is the time, in years.

Two unknowns, but P drops out showing:

2 = (1+i)^t

Plug in i, solve for t.

I got 11.43 years.

You have the right formula for continuous compounding, except P should be 2P and A should be P.

If the interest rate compounds anything other than yearly, and you need to find the time in years, you can find the effective interest rate in years using:

ia = (1+r/m)^m - 1,

where is = effective interest rate, r = nominal interest rate, and m = compounding periods per year.