Final answer:
The annual 401(k) investment is $23,800, considering an individual contribution plus the company match. The one-year return is approximately 10.995 percent. Moreover, examples demonstrate the power of compound interest over time with and without administrative fees.
Step-by-step explanation:
The annual investment in the 401(k) plan can be calculated by taking 10 percent of the $136,000 annual income, which amounts to $13,600. The company match, which is 75 percent of the first 10 percent, comes to an additional $10,200 (0.75 * $13,600). Therefore, the total annual investment including the company match is $13,600 + $10,200 = $23,800.
The one-year return in percentage is based on the expected fund yield of 11 percent. Since the investment is $23,800, the return in one year would be 11 percent of that, which is $2,618. Therefore, the percentage return on the total investment is ($2,618 / $23,800) which is approximately 10.995 percent when rounded to three decimal places.
To understand the power of compound interest, let's consider the given example of retirement savings. If Alexx and Spenser each invest $5,000 with an annual return of 5 percent for Alexx and 4.75 percent for Spenser (due to a 0.25 percent fee), after 30 years, Alexx's investment would have grown more due to not having the administrative fee subtracted. Similarly, saving $3,000 at an assumed 7 percent rate of return would grow substantially over 40 years due to compounding, as illustrated by the provided formula.