# SOLUTION: How long will it take an investment to double if it is invested at a 5% annual interest rate and compounded continuously? So, I'm really drawing a complete blank on this, i know

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**Question 313164.**

*How long will it take an investment to double if it is invested at a 5% annual interest rate and compounded continuously?*

*So, I'm really drawing a complete blank on this, i know P=e^rt, so P=e^0.05t, but that's far as I got. Thanks!*

**Found 2 solutions by solver91311, nerdybill. Answer by solver91311(20203) You can put this solution on YOUR website!**

So far, so good, except for one tiny detail. The formula you want is:

Where is the amount at the end, is what you start with, is the rate as decimal, is the time in years, and is the base of the natural logarithms.

Since you want your money to double,

Therefore:

You don't need to substitute the

rate value just yet. patience, Grasshopper.

Take the natural logarithm of both sides:

Next apply the following rule:

Next use the fact that

Since you want to know , multiply both sides by

NOW substitute the value of

And finally get all happy with your calculator

years.

By the way, this same formula will work for "How long will it take my money to multiply by at interest rate compounded continuously.

John

**Answer by** **nerdybill(7375)** You can put this solution on YOUR website!

How long will it take an investment to double if it is invested at a 5% annual interest rate and compounded continuously?

You forgot the "initial principal" in your formula.

Po is the initial investment

Source: www.algebra.comCategory: Bank

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