Final answer:
The effective annual yield on a long-term investment in a diversified stock portfolio starting with $3,000 could reach $44,923 after 40 years with a 7% annual return rate. Buying a bond for $964 and receiving a total of $1,080 at maturity results in a 12% yield. The safest and riskiest investments would depend on their volatility and guaranteed returns.
Step-by-step explanation:
To determine the effective annual yield for each investment and select the better investment, one would need to calculate the total return, considering interest payments and any capital gains over the period. In the given example, if you save $3,000 at age 25 in an account with a 7% real annual rate of return, after 40 years, the investment would have grown to $44,923, showing the power of compound interest.
Regarding the bond investment, if an investor purchases a bond for $964 and receives the $1,000 face value plus an $80 interest payment at the end, the yield would be calculated as follows: ($1080 - $964)/$964 = 12%. This reflects both the interest payments and the capital gains from the investment.
To identify which investment is safest, one might consider the volatility and guarantee of returns; typically, bonds are considered safer with fixed interest rates, whereas stock portfolios can be riskier due to market fluctuations. The riskiest investment is generally the one with higher volatility and less guaranteed returns. The investment with the highest expected return would be the one with the highest annual yield calculated.
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