Suppose an investment offers to triple your money in 48 months (don't believe it). What rate of return per quarter are you being offered?



To determine the rate of return per quarter that results in tripling the investment over 48 months, we can use the compound interest formula:

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

Where:
- \(A\) is the final amount (3 times the initial investment, or \(3P\)),
- \(P\) is the initial investment,
- \(r\) is the quarterly rate of return we need to find,
- \(n\) is the number of compounding periods (48 months = 16 quarters).

Now, substituting the known values into the formula:

\[
3P = P(1 + r)^{16}
\]

Dividing both sides by \(P\):

\[
3 = (1 + r)^{16}
\]

To solve for \(r\), take the 16th root of both sides:

\[
1 + r = \sqrt[16]{3}
\]

Then subtract 1 from both sides:

\[
r = \sqrt[16]{3} - 1
\]

Now, let's calculate the value of \(r\).

\[
r \approx 1.07177 - 1 = 0.07177
\]

Thus, the quarterly rate of return is approximately **7.18%**.

Would you like more details or have any other questions?

### Related Questions:
1. How would the calculation change if the investment doubled in 48 months instead of tripling?
2. What is the annual rate of return equivalent to this quarterly rate?
3. How does this rate compare to typical investment returns?
4. What is the monthly rate of return for this investment?
5. How much time would it take to quadruple your investment at this quarterly rate?

### Tip:
Always be cautious of offers promising unusually high returns—such promises often come with high risks or hidden downsides.

Suppose an investment offers to triple your money in 48 months (don't believe it). What rate of return per quarter are you being offered?

Discover how to calculate the quarterly rate of return needed to triple an investment in 48 months. This detailed solution uses the compound interest formula and exponential growth principles, ideal for students in Grades 10-12 or anyone learning about financial mathematics.

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