How long will it take money to triple at an APR of 6.7​% compounded​ annually?
(Round up to the nearest​ year.)

To calculate how long it will take for the money to triple at an APR of 6.7% compounded annually, we can use the compound interest formula:

\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]

Where:
- \( A \) is the final amount (in this case, triple the original, so \( A = 3P \)),
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (6.7% or 0.067),
- \( n \) is the number of times the interest is compounded per year (annually, so \( n = 1 \)),
- \( t \) is the time in years.

We need to solve for \( t \). Start by simplifying the formula:

\[
3P = P \left( 1 + \frac{0.067}{1} \right)^{1 \cdot t}
\]

Since \( P \) cancels out on both sides:

\[
3 = \left( 1.067 \right)^t
\]

Now, take the natural logarithm of both sides to solve for \( t \):

\[
\ln(3) = t \cdot \ln(1.067)
\]

Solving for \( t \):

\[
t = \frac{\ln(3)}{\ln(1.067)}
\]

Let me calculate that.It will take approximately **17 years** for the money to triple at an APR of 6.7% compounded annually.

Would you like more details or have any questions about the calculation?

Here are 5 related questions to consider:
1. How would the time change if the interest rate was higher or lower?
2. What if the interest were compounded monthly instead of annually?
3. How would the result differ if we wanted the money to quadruple instead of triple?
4. What is the difference between simple interest and compound interest in long-term investments?
5. How can you calculate the amount of money after a given number of years for a fixed interest rate?

**Tip:** The natural logarithm function (\( \ln \)) is often used in compound interest problems to solve for time, as it helps unravel exponential growth.

How long will it take money to triple at an APR of 6.7% compounded annually? (Round up to the nearest year.)

Learn how to calculate the time it takes for money to triple at an APR of 6.7% compounded annually. Using the compound interest formula and logarithms, this step-by-step solution is perfect for high school students studying exponential growth and interest rates.

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