To solve the questions:

a. Per annum simple rate of return

The formula for the simple interest rate is:

$A = P(1 + rt)$

Where:

• $A$ is the terminal account balance ($4100)
• $P$ is the initial investment ($1000)
• $r$ is the annual simple interest rate
• $t$ is the time in years (10 years)

Rearranging for $r$:

$r = \frac{A - P}{Pt}$

Substitute the given values:

$r = \frac{4100 - 1000}{1000 \cdot 10}$

$r = \frac{3100}{10000} = 0.31$

So, the simple rate of return per annum is:

$r = 31\%$

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b. Continuous rate of return per annum

The formula for continuous compounding is:

$A = Pe^{rt}$

Rearranging for $r$:

$r = \frac{\ln(A/P)}{t}$

Substitute the given values:

$r = \frac{\ln(4100/1000)}{10}$

$r = \frac{\ln(4.1)}{10}$

$r = \frac{1.411}{10} = 0.1411$

So, the continuous rate of return per annum is:

$r \approx 14.11\%$

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Final Answers:

a. Per annum simple rate of return: 31%
b. Continuous rate of return per annum: 14.11%

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Would you like further explanation or details about these calculations?
Here are five related questions to explore further:

1. What is the difference between simple and continuous interest rates in practice?
2. How would the calculations change if the investment duration was 15 years instead of 10?
3. What is the formula for annual compounding, and how does it compare to continuous compounding?
4. How does the investment's terminal balance vary with different initial investments for the same interest rate?
5. Can continuous compounding exceed simple interest significantly over short timeframes?

Tip: Always double-check which compounding method applies in investment scenarios to avoid misinterpretations