Mpho saved P1200, and plans to put it into an investment earning 6% interest. How many 
years will it take Mpho to triple her money?

To determine how long it will take for Mpho's investment to triple at a 6% annual interest rate, we can use the formula for compound interest. Since the problem doesn't specify whether the interest is compounded annually, monthly, or continuously, I'll assume it's compounded annually for simplicity.

The formula for compound interest is:

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

Where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed for.

However, since Mpho wants to triple her money, we can set \( A = 3P \). This simplifies to:

\[
3P = P \left(1 + \frac{r}{n}\right)^{nt}
\]

By dividing both sides by \( P \), we get:

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

Since we're assuming the interest is compounded annually (\( n = 1 \)), the formula simplifies to:

\[
3 = (1 + r)^t
\]

Substituting \( r = 0.06 \) (since 6% interest is 0.06 as a decimal):

\[
3 = (1.06)^t
\]

To solve for \( t \), we'll take the natural logarithm (ln) of both sides:

\[
\ln(3) = \ln((1.06)^t)
\]

Using the logarithm power rule:

\[
\ln(3) = t \cdot \ln(1.06)
\]

Finally, solve for \( t \):

\[
t = \frac{\ln(3)}{\ln(1.06)}
\]

Let's calculate this.

\[
t \approx \frac{1.0986}{0.0583} \approx 18.84 \text{ years}
\]

So, it will take approximately **18.84 years** for Mpho to triple her money with a 6% annual interest rate.

Would you like further details on this calculation, or do you have any other questions?

### Related Questions:
1. What if the interest was compounded monthly instead of annually?
2. How long would it take for the money to quadruple at the same interest rate?
3. What is the effect of increasing the interest rate to 8% on the time needed to triple the investment?
4. How would the time change if Mpho wanted to double her money instead of tripling it?
5. What is the present value needed to achieve a certain amount after a fixed time period with a 6% interest rate?

### Tip:
Remember that the higher the interest rate or the more frequent the compounding period, the less time it will take for an investment to grow to a desired amount.

Mpho saved P1200, and plans to put it into an investment earning 6% interest. How many years will it take Mpho to triple her money?

Discover how long it will take for Mpho to triple her P1200 investment at a 6% annual interest rate using the compound interest formula. This detailed solution involves exponential growth concepts and logarithms, suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation