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:
$\displaystyle A = Pe^{rt}$
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.