how long will it take an investment of $1,750 to double in value at 8% annual interest compounded continuously?
e^(.08t) = 2
The initial amount does not matter.
To calculate the time it will take for an investment to double in value at a given interest rate compounded continuously, you can use the formula:
t = ln(2) / (r * ln(e))
Where:
- t is the time in years
- ln is the natural logarithm
- r is the interest rate expressed as a decimal
- e is the mathematical constant approximately equal to 2.71828
In this case, the interest rate is 8% per year, which can be written as 0.08.
Plugging these values into the formula:
t = ln(2) / (0.08 * ln(e))
Now we can evaluate the expression:
t ≈ 0.6931 / (0.08 * 1)
Simplifying further:
t ≈ 0.6931 / 0.08
t ≈ 8.66375
Therefore, it will take approximately 8.66 years for an investment of $1,750 to double in value at an 8% annual interest rate compounded continuously.