Kyle And Wes: Two Savings Strategies For Friends

Kyle And Wes Two Savings Strategies Two Friends Kyle And Wes Graduat

Kyle and Wes, two friends, both began their careers at age 25. Kyle started contributing $100 monthly to his 401(k) immediately upon becoming eligible, for a period of ten years. After ten years, Kyle stopped investing but left his accumulated balance untouched. Wes, however, chose to spend his early income on lifestyle expenses and did not invest immediately. Instead, he began monthly contributions of $100 to his 401(k) after ten years, continuing for a further twenty years. Both friends' investments earned an average annual return of 8%. The goal is to analyze their investment growth and compare their retirement savings, focusing on total contributions, accumulated balances, and the implications of investment timing and compound interest.

Paper For Above instruction

Understanding the power of compound interest and the influence of investment timing, this case study compares the retirement savings trajectories of two friends, Kyle and Wes, who adopted different investment strategies. By examining their contributions, growth, and eventual balances, we can shed light on the importance of early and consistent investing, as well as the value of patience and timing in wealth accumulation.

Contribution Analysis

Initially, Kyle contributed $100 monthly for ten years. Each contribution is made well before the present, so total contributions over this period are calculated straightforwardly: 10 years × 12 months/year × $100/month = $12,000. Wes, who delayed his investment, started contributing after ten years, and his contributions continued for 20 years: 20 years × 12 months/year × $100/month = $24,000. Summing contributions provides a baseline for total investment: Kyle $12,000, Wes $24,000.

Kyle’s Investment Growth after 10 Years

Using the future value of an annuity formula, the value of Kyle's investments after ten years can be calculated with an 8% annual return, compounded monthly. The formula for future value (FV) of a series of monthly payments (PMT) over n months is: FV = PMT × [(1 + r)^n - 1] / r, where r is the monthly interest rate (annual rate divided by 12). r = 0.08 / 12 ≈ 0.0066667, n = 10 × 12 = 120 months.FV = 100 × [(1 + 0.0066667)^120 - 1] / 0.0066667 ≈ 100 × [2.707 - 1] / 0.0066667 ≈ 100 × 256.356 ≈ $25,635.60.

Kyle’s Balance After 20 More Years of Growth

Next, to find Kyle’s balance after twenty more years of growth without additional contributions, we treat his ten-year accumulated amount as a lump sum that continues to grow at 8%. Using the compound interest formula: FV = PV × (1 + r)^t, where PV is the present value, r is the annual rate, and t is the number of years. PV = $25,635.60, r = 0.08, t = 20. FV = 25,635.60 × (1 + 0.08)^20 ≈ 25,635.60 × 4.660 ≈ $119,513.55.

Growth of Kyle’s Investment

Over the twenty-year period, Kyle's investment grew from approximately $25,636 to about $119,514, primarily due to the power of compound interest and the early start. This demonstrates how initial contributions, coupled with time, can significantly amplify wealth without further injections.

Wes’s Total Investment after 20 Years

Wes’s contributions of $100 monthly over twenty years amount to $24,000. Unlike Kyle, Wes's investments only accrue interest from the point he begins investing at year ten. His initial ten-year period had no contributions, so his total contributions are straightforward: $24,000.

Comparative Analysis of Final Balances

To determine Wes’s final balance at the end of twenty years of investing, we again use the future value of an annuity formula for 20 years of contributions starting at year 10. The calculation aligns with Kyle's, but begins after a ten-year delay. First, find the accumulated amount at the end of year 30 using the same annuity FV formula for 20 years: FV = 100 × [(1 + 0.0066667)^240 - 1] / 0.0066667 ≈ 100 × [9.646 - 1] / 0.0066667 ≈ 100 × 1320.779 ≈ $132,077.90. But this is at year 30, so to find Wes’s balance at year 55, we compound this amount for another 25 years: FV = 132,077.90 × (1 + 0.08)^25 ≈ 132,077.90 × 6.848 ≈ $904,867.45.

Who Has the Higher Balance?

Comparing the two final balances: Kyle has approximately $119,514, while Wes’s balance is approximately $904,867. Welsey’s delayed start significantly hindered his growth, despite higher total contributions, illustrating the critical impact of earlier investment and the time value of money.

Implication of Investment Timing and the Time Value of Money

This comparison underscores that early and consistent investing yields substantially greater wealth over the long term due to compounding. Kyle’s early start allowed his investments to grow exponentially, even with smaller total contributions. In contrast, Wes’s later start, even with comparable monthly contributions, resulted in a much larger final amount, primarily due to the extended growth period starting from a larger base. This exercise vividly demonstrates that time is a valuable asset in wealth accumulation, emphasizing the importance of starting to invest early regardless of the initial amount.

Conclusion

The exercise illustrates that making consistent investments early can leverage the power of compound interest to build wealth more effectively than delayed contributions. Kyle’s disciplined early contributions, even with a modest amount, grew significantly over time, whereas Wes’s late start resulted in a comparatively modest final balance despite larger contributions. Therefore, individuals aiming for long-term financial security should prioritize early and consistent saving strategies.

References

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