Question

Inez bought 100 shares of a mutual fund for \(\$ 10\) each and sold them five years later for \(\$ 15\) each. Ethan put \(\$ 1,000\) in a 5 -year \(\mathrm{CD}\) and received a total of \(\$ 235\) in interest. Which investment provided the better return? How does this illustrate the relationship between risk and return?

Short answer

Inez's investment had a better return of 50% compared to Ethan's 23.5%. Higher returns often mean higher risk, as seen with stock investments versus CDs.

Step-by-step solution

Calculate Initial and Final Amounts for Inez

Inez bought 100 shares at \(10 each, so her initial investment was \( 100 \times 10 = \\)1000 \). She sold them for \(15 each, so her final amount was \( 100 \times 15 = \\)1500 \).

Calculate Profit and Return for Inez

The profit Inez made was \( \\(1500 - \\)1000 = \\(500 \). To find the return, use the formula: \( \text{Return} = \frac{\text{Profit}}{\text{Initial Investment}} \times 100\% \). So, the return is \( \frac{\\)500}{\$1000} \times 100\% = 50\% \).

Calculate Initial and Final Amounts for Ethan

Ethan invested \\(1000 in a CD and received \\)235 in interest. His final amount was \( \\(1000 + \\)235 = \$1235 \).

Calculate Return for Ethan

The profit for Ethan was \( \\(235 \). Return is calculated as \( \text{Return} = \frac{\text{Profit}}{\text{Initial Investment}} \times 100\% \). So, Ethan's return is \( \frac{\\)235}{\$1000} \times 100\% = 23.5\% \).

Compare Returns and Discuss Risk vs. Return

Inez's investment had a return of 50%, while Ethan's had a return of 23.5%. Inez's higher return also comes with higher risk since stock values can fluctuate, whereas Ethan’s CD is lower risk but offers a lower return, illustrating that higher potential returns are typically associated with higher risk investments.

Key concepts

Investment Returns

Investment returns are essential in evaluating how well an investment has performed over time. They look at the financial growth of an investment from when it was initially made until it was sold or matured. This concept helps investors determine the profitability of their investments.

To calculate investment returns, you need to know the initial investment amount, final value, and profit. The formula is:

• Return = \( \left( \frac{\text{Final Value} - \text{Initial Investment}}{\text{Initial Investment}} \right) \times 100\% \)

For example, Inez’s initial investment in mutual fund shares was \( \\(1000 \) and she sold them for \( \\)1500 \). Her profit was \( \\(500 \), resulting in a return of 50%. On the other hand, Ethan's \( \\)1000 \) CD provided \( \$235 \) interest, giving a return of 23.5%.

Mutual Funds vs CDs

When choosing between mutual funds and CDs, it's important to understand the differences. Both are investment options with varying levels of risk and return.

Mutual funds involve pooling money from multiple investors to purchase a diversified portfolio of stocks, bonds, or other securities. They can provide high returns due to their diversified nature and active management, but also come with higher risk. In Inez's case, investing in mutual funds gave her a higher return of 50%, but with the risk that the value of shares might fluctuate over time.

Certificates of Deposit (CDs) are savings certificates with a fixed maturity date and interest rate. They are considered low-risk investments as the principal is usually insured. CDs offer stability and a guaranteed return, but generally at a lower rate, as Ethan experienced with a 23.5% return over five years. CDs are ideal for conservative investors seeking stable returns.

Risk Assessment

Risk assessment in investments involves evaluating the uncertainty and potential financial loss associated with an investment choice. It's a critical component for making informed investment decisions.

Investments like mutual funds carry higher risk due to their exposure to market volatility and economic fluctuations. Risk can impact returns significantly, both positively and negatively. Hence, higher risk investments, such as Inez's mutual fund, tend to offer higher returns to compensate for the potential losses.

Conversely, low-risk investments like CDs offer more security with minimal fluctuation in returns. Ethan’s investment in a CD guaranteed his principal plus interest, making it safer, albeit with a lower return. Investors must balance their risk tolerance with their desired returns when assessing investment options.

Financial Decision Making

Financial decision making in investments involves weighing the potential risks and rewards to make sound choices. Investors need to decide based on their financial goals, risk appetite, and investment horizon.

One must gather and analyze financial information about various investment options. This includes understanding historical performance, fees, and market conditions. For Inez and Ethan, their decisions reflect different strategies: Inez chose a higher-risk, higher-reward method with mutual funds, while Ethan opted for the certainty of a lower-risk CD.

A good financial decision aligns with personal financial goals while considering the trade-off between risk and return. Regularly reviewing investment performance, like calculating returns, helps investors to adjust strategies as needed. This approach ensures that investments remain aligned with evolving financial objectives.