Carl plans to invest $500 at 8.25% interest, compounded continuously. How long will it take for his money to triple?
To find the time it takes for the money to triple, we use the continuous compounding formula:
[ A = P \times e^{rt} ]
Where:
- ( A ) is the amount of money after time ( t )
- ( P ) is the principal amount (initial investment)
- ( r ) is the annual interest rate (in decimal form)
- ( t ) is the time in years
- ( e ) is Euler's number (approximately 2.71828)
Given:
- ( P = $500 )
- ( r = 8.25% ) (convert to decimal: ( 0.0825 ))
- We want ( A ) to be triple the initial investment, so ( A = 3P = 3 \times 1500 )
Substituting the values into the formula, we have:
[ 1500 = 500 \times e^{0.0825t} ]
Now, solve for ( t ):
[ \frac{1500}{500} = e^{0.0825t} ]
[ 3 = e^{0.0825t} ]
Taking the natural logarithm (ln) of both sides to isolate ( t ):
[ \ln(3) = 0.0825t ]
[ t = \frac{\ln(3)}{0.0825} ]
[ t \approx \frac{1.0986}{0.0825} ]
[ t \approx 13.31 \text{ years} ]
So, it will take approximately 13.31 years for Carl's money to triple at an interest rate of 8.25%, compounded continuously.
By signing up, you agree to our Terms of Service and Privacy Policy
In our example:
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7