Alice invests some money into an account that pays 4%
 compound interest per annum.

Work out after how many years Alice will have trebled the investment.

Given:
- Compound interest rate (\( r \)) = 4% per annum.
- Alice wants to triple her investment, so the final amount (\( A \)) will be 3 times the initial amount (\( P \)).

The formula for compound interest is:

\[
A = P(1 + r)^n
\]

Where:
- \( A \) is the final amount.
- \( P \) is the initial investment.
- \( r \) is the interest rate per period.
- \( n \) is the number of periods (years in this case).

Since \( A = 3P \) and \( r = 0.04 \) (4% expressed as a decimal), we substitute into the formula:

\[
3P = P(1 + 0.04)^n
\]

Divide both sides by \( P \) to simplify:

\[
3 = (1.04)^n
\]

To solve for \( n \), take the natural logarithm of both sides:

\[
\ln(3) = \ln((1.04)^n)
\]

Apply the logarithmic rule: \( \ln(a^b) = b \ln(a) \):

\[
\ln(3) = n \ln(1.04)
\]

Now, solve for \( n \):

\[
n = \frac{\ln(3)}{\ln(1.04)}
\]

Let's calculate this value:

The number of years it will take for Alice's investment to triple at a 4% annual compound interest rate is approximately 28 years.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. What would happen if the interest rate was compounded monthly instead of annually?
2. How long would it take for Alice's investment to double at the same interest rate?
3. How does the compounding frequency affect the time it takes to triple an investment?
4. What if Alice wanted to quadruple her investment instead? How many years would that take?
5. How can you adjust the formula if a different interest rate is used?

**Tip:** Compounding frequency (e.g., annually, monthly) can significantly impact how quickly an investment grows.

Alice invests some money into an account that pays 4% compound interest per annum. Work out after how many years Alice will have trebled the investment.

Discover how to calculate the time required for Alice’s investment to triple at a 4% annual compound interest rate. This solution uses logarithms and the compound interest formula to determine that it will take approximately 28 years. Perfect for students in Grades 9-12 interested in financial mathematics.

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