A company offers two investment plans. Plan A offers a fixed interest rate of 5% per annum compounded annually, while Plan B offers a fixed interest rate of 4.5% per annum compounded semi-annually. If an investor invests $1,000 in each plan, which plan yields more after 3 years, and by how much?

["Choosing the Better Investment: Fixed Rates: Plan A vs Plan B After 3 Years", "When planning long-term investments, understanding the impact of interest rates and compounding frequency is crucial. For investors considering two options, choosing the right plan can significantly affect returns. In this article, we compare two investment plans with distinct compounding schedules to determine which delivers higher returns after 3 years.", "---", "Plan A: 5% Annual Compound Interest\n- Annual interest rate: 5%\n- Compounding frequency: Annually\n- Investment: $1,000", "Plan B: 4.5% Annual Compound Interest (semi-annually)\n- Annual interest rate: 4.5%\n- Compounding frequency: Semi-annually (twice per year)\n- Investment: $1,000", "---", "How Interest Compounding Works", "Compounding frequency affects how often interest is calculated and added to the principal. More frequent compounding generally increases returns because interest earns interest sooner.", "For Plan A:\nInterest compounds once per year.\nAfter 3 years, the formula for compound interest is:\n[\nFV = P \left(1 + \frac{r}{n_{\ ext{annual}}}\right)^{r \ imes t}\n]\nWhere:\n- ( P = 1000 )\n- ( r = 0.05 )\n- ( n_{\ ext{annual}} = 1 )\n- ( t = 3 )", "[\nFV_A = 1000 \left(1 + \frac{0.05}{1}\right)^{3} = 1000 \ imes (1.05)^3 = 1000 \ imes 1.157625 = 1157.63\n]", "For Plan B:\nInterest compounds twice per year (semi-annually).\n[\nFV = P \left(1 + \frac{r}{n_{\ ext{semi}}}\right)^{n_{\ ext{semi}} \ imes t}\n]\nWhere:\n- ( r = 0.045 )\n- ( n_{\ ext{semi}} = 2 )\n- ( t = 3 )", "[\nFV_B = 1000 \left(1 + \frac{0.045}{2}\right)^{2 \ imes 3} = 1000 \left(1 + 0.0225\right)^6 = 1000 \ imes (1.0225)^6\n]", "Now calculate ( 1.0225^6 ):\nUsing step-by-step compounding:\n( 1.0225^6 \approx 1.143041 )", "[\nFV_B \approx 1000 \ imes 1.143041 = 1143.04\n]", "---", "Comparison After 3 Years", "- Plan A (5% annually): $1,157.63\n- Plan B (4.5% semi-annually): $1,143.04", "Difference:\n[\n1157.63 - 1143.04 = 14.59\n]", "---", "Conclusion", "After 3 years, Plan A with a 5% fixed interest rate compounded annually yields more than Plan B. Investors gain $14.59 by choosing Plan A due to the higher nominal rate, even though Plan B compounds more frequently.", "If steady returns are your priority and you value simplicity in compounding, Plan A outperforms in this scenario. However, for long-term growth with slightly lower interest but frequent compounding, Plan B offers modest advantages—this example clearly favors Plan A.", "Invest wisely by comparing not just rates, but compounding methods to maximize returns.", "---", "Keywords: Investment comparison, fixed interest rate, compound interest, Plan A 5%, Plan B 4.5% semi-annual, better investment 2024, compounding frequency, long-term investing, return analysis, $1,000 investment, growth calculation"]