# Compounded Continuously

• Aug 11th 2008, 04:53 AM
magentarita
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.
• Aug 11th 2008, 05:26 AM
Simplicity
Quote:

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.
• Aug 11th 2008, 09:05 PM
magentarita
Air...
Air, you are a great math professor!