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.

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- Aug 11th 2008, 04:53 AMmagentaritaCompounded 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 AMSimplicity
The continuous compound interest formula is:

$\displaystyle A = Pe^{rt}$

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:

$\displaystyle 25000= 10000e^{0.06t}$

Now, solve for $\displaystyle t$ 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 PMmagentaritaAir...
Air, you are a great math professor!