# Math Help - Compounded Continuously

1. ## Compounded Continuously

How many years will it take for an initial investment of $10,000 to grow to$25,000? Assume a rate of interest of 6% compounded continuously.

2. Originally Posted by magentarita
How many years will it take for an initial investment of $10,000 to grow to$25,000? Assume a rate of interest of 6% compounded continuously.
The continuous compound interest formula is:

$A = Pe^{rt}$

Where:
• P = Principal amount (initial investment)
• r = Annual interest rate (as a decimal)
• t = Number of years
• A = Amount after time t
• e = Exponential function

From the question, we can deduce that P=$10,000, r=0.06, t=?, A=$25,000 and hence inserting the values into the formula gives:

$25000= 10000e^{0.06t}$

Now, solve for $t$ and you will have the amount of years for the investment to grow from $10000 to$25000 with continuous compound interest.

3. ## Air...

Air, you are a great math professor!