Question

Euler Bank advertises that it compounds interest continuously and that it will double your money in 20 yr. What is the annual interest rate?

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You must apply the following formula:

$FV=(PV)(e^{it})$

Where $FV$ is the future value, $PV$ is the present value, $i$ is the interest rate and $t$ is the time in years.

2. You have that the bank will double your money in $20$ years. Therefore:

$FV=2PV$

3. Substitute values into the formula and solve for $i$, as following:

$2PV=(PV)(e^{(i)(20)} \\ 2=e^{(i)(20)}$

4. By applying natural logarithm, you have:

 $ln(2)=(i)(20) \\ i= \frac{ln(2)}{20} \\ i=0.0346$

 $i=3.46$ %

 The answer is: $3.46$ %