To determine the return (rate of return) of the higher-risk investment, we will use the formula for compound interest:

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

Where:

• $A$ is the future value (payoff),
• $P$ is the initial investment (buy-in),
• $r$ is the annual interest rate (what we are solving for),
• $n$ is the number of compounding periods per year (quarterly means $n = 4$),
• $t$ is the time in years.

Step 1: Identify the higher-risk investment

Based on the scenario, the risk level isn't explicitly stated. However, typically, the smaller the initial investment, the higher the risk, so we assume Investment B is the higher-risk one.

Step 2: Apply the compound interest formula to Investment B

For Investment B:

• $A = 7,182$ (future value),
• $P = 468$ (initial investment),
• $n = 4$ (quarterly compounding),
• $t = 16$ (total time from buy-in to payoff: 4 years ago + 12 years into the future).

The formula becomes: $7,182 = 468 \left(1 + \frac{r}{4}\right)^{4 \times 16}$ Simplifying: $7,182 = 468 \left(1 + \frac{r}{4}\right)^{64}$

Step 3: Solve for $r$

We will now solve for $r$, the annual rate of return. Let's compute this.The return of the higher-risk investment (Investment B) is approximately 17.44%.

Do you want more details or have any questions?

Here are 5 related questions to explore:

1. How would the return change if the buy-in for Investment B was higher?
2. What is the return of Investment A under similar calculations?
3. How does the compounding frequency affect the rate of return?
4. Can we use the same formula for monthly or yearly compounding periods?
5. What factors generally make an investment high-risk?

Tip: The more frequent the compounding periods (e.g., quarterly vs. annually), the higher the effective interest rate for the same nominal rate.