Create A Table Showing FV At 0, 5, And 20 For 0–4

Create A Table That Shows The Fv At 0 5 And 20 For 0 1 2 3 4

Create a table that shows the future value (FV) at interest rates of 0%, 5%, and 20% for different periods of 0, 1, 2, 3, 4, and 5 years. Use an initial amount of $1,610.51. The interest rates are applied annually, and the FV is calculated using the formula: FV = PV × (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of years.

Paper For Above instruction

Financial calculations such as determining the future value (FV) of an investment are fundamental in personal finance, investment planning, and economic analysis. The FV provides insight into how an initial amount accrues over time under various interest rates, enabling individuals and organizations to make informed decisions about saving and investing. This paper examines the calculation of FV across different interest rates and time horizons, specifically focusing on rates of 0%, 5%, and 20% over periods of 0 to 5 years, based on a principal amount of $1,610.51.

To construct the relevant tables, the key formula used is FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate expressed in decimal form, and n is the number of years. This formula assumes compounded interest, which is standard in financial calculations. It highlights how the investment's value grows over time depending on the rate at which interest is earned and compounded annually.

Starting with the principal amount of $1,610.51, calculations are performed for each interest rate over the specified periods. For an interest rate of 0%, the FV remains the same regardless of the number of years, as there is no growth. For 5% and 20%, the FV increases exponentially as the number of years increases, illustrating the power of compounding.

The calculations for each interest rate and year are as follows:

  • At 0% interest:
  • n=0: FV = 1610.51 × (1 + 0)^0 = 1610.51
  • n=1: FV = 1610.51 × (1 + 0)^1 = 1610.51
  • n=2: FV = 1610.51 × (1 + 0)^2 = 1610.51
  • ... and similarly for 3, 4, and 5 years.
  • At 5% interest:
  • n=0: FV = 1610.51 × (1 + 0.05)^0 = 1610.51
  • n=1: FV = 1610.51 × (1 + 0.05)^1 ≈ 1690.04
  • n=2: FV ≈ 1774.54
  • n=3: FV ≈ 1863.27
  • n=4: FV ≈ 1956.44
  • n=5: FV ≈ 2054.26
  • At 20% interest:
  • n=0: FV = 1610.51 × (1 + 0.20)^0 = 1610.51
  • n=1: FV ≈ 1933.61
  • n=2: FV ≈ 2319.33
  • n=3: FV ≈ 2783.20
  • n=4: FV ≈ 3339.84
  • n=5: FV ≈ 4007.81

Constructing a table from these calculations provides a clear visualization of how different interest rates impact the growth of an initial investment over time. The exponential growth at higher interest rates demonstrates the importance of compounding in wealth accumulation.

In conclusion, understanding how FV varies with interest rate and time is crucial for making informed financial decisions. By evaluating these calculations across different scenarios, investors can better assess the potential outcomes of their investments and choose strategies aligned with their financial goals.

References

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  • Investopedia. (2021). Compound Interest Definition. https://www.investopedia.com/terms/c/compoundinterest.asp
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  • Investopedia. (2020). Future Value (FV): Definition and How to Calculate. https://www.investopedia.com/terms/f/futurevalue.asp

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