What Is The Future Value Of $2,944 Invested For 9 Years At 6

What Is The Future Value Of 2944 Invested For 9 Years At 600 Percen

What is the future value of $2,944 invested for 9 years at 6.00 percent compounded annually? Additionally, if you invested $3,140 a year ago and now your investment is worth $3,700.50, what interest rate did you earn? Consider Julie’s land investment: she purchased eleven acres costing $15,190, and today the land is valued at $59,547. How long has she owned this land if the land appreciated at 5 percent annually? Furthermore, compare simple and compound interest by analyzing deposits: if you deposited $61,000 in First City Bank earning 8% simple interest and in Second City Bank earning 8% compounded annually, how much more money would you have with the compound interest after 8 years? Calculate the future value of $1,000 compounded annually for periods of 20, 15, and 25 years at rates of 6%, 9%, and 6%, respectively. Also, determine the present value of a series of cash flows with varying discount rates, and analyze the investment project with given cash flows discounted at 7%, 18%, and 24%. Finally, assess stock investment returns: calculate total dollar return from stock sales and dividends, and determine the percentage total return given initial and ending share prices and dividends. Additionally, compute the average real return and the average nominal risk premium of SkyNet Data Corporation’s stock over five years, considering inflation and T-bill rates.

Paper For Above instruction

The inquiry begins by evaluating the future value (FV) of an investment amount of $2,944 over a period of nine years at an interest rate of 6 percent compounded annually. The formula for compound interest FV is given by:

FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years. Substituting the known values: FV = 2944 × (1 + 0.06)^9 ≈ 2944 × 1.689479 ≈ $4,976.66. This indicates that a $2,944 investment would grow to approximately $4,976.66 after nine years at 6 percent annually.

Next, considering a previous investment of $3,140 made one year ago that is now worth $3,700.50, we can determine the annual interest rate earned using the formula for future value growth:

FV = PV × (1 + r)^n. Solving for r gives:

r = (FV / PV)^(1/n) - 1. Here, r = (3700.50 / 3140)^(1/1) - 1 ≈ 1.1799 - 1 ≈ 0.1799 or 17.99%. Thus, the investment earned approximately 18 percent interest over the year.

Regarding Julie's land investment, she purchased eleven acres for $15,190, and the current valuation is $59,547. To determine how long she has owned this land, assuming an annual appreciation rate of 5 percent, the future value formula is used:

FV = PV × (1 + g)^t, solving for t: t = log(FV / PV) / log(1 + g). Substituting gives: t = log(59547 / 15190) / log(1.05) ≈ log(3.922) / 0.02119 ≈ 0.593 / 0.02119 ≈ 27.97 years. Consequently, Julie has owned the land for approximately 28 years.

The comparison between simple and compound interest investments involves depositing $61,000 in each bank, both earning 8 percent, but with different interest calculations over eight years. For the simple interest account:

Amount = Principal + (Principal × rate × time) = 61,000 + (61,000 × 0.08 × 8) = 61,000 + 38,880 = $99,880.

For the compound interest account, the future value is computed as:

FV = PV × (1 + r)^n = 61,000 × (1 + 0.08)^8 ≈ 61,000 × 1.85093 ≈ $112,996.66.

Therefore, the additional earnings from the compounded account are approximately:

$112,996.66 - $99,880 ≈ $13,116.66.

Various calculations of future values (FV) for different periods and rates are as follows:

  • 20 years at 6%: FV = 1000 × (1 + 0.06)^20 ≈ 1000 × 3.2071 ≈ $3,207.14
  • 15 years at 9%: FV = 1000 × (1 + 0.09)^15 ≈ 1000 × 3.6425 ≈ $3,642.50
  • 25 years at 6%: FV = 1000 × (1 + 0.06)^25 ≈ 1000 × 4.2919 ≈ $4,291.88

For present value (PV) calculations with known future values (FV), years, and interest rates, the formula used is:

PV = FV / (1 + r)^n. For example, if FV is $15,164 over certain years at various interest rates, PV can be computed accordingly once all data are specified.

The valuation of an investment project by present value involves discounting future cash flows using a discount rate. For cash flows of $350 in Year 1 with rates of 7%, 18%, and 24%, the present values are computed as:

PV = Cash Flow / (1 + rate)^n. At 7%: PV ≈ 350 / 1.07 ≈ $327.10

At 18%: PV ≈ 350 / 1.18 ≈ $296.61

At 24%: PV ≈ 350 / 1.24 ≈ $282.26

Analyzing stock investment returns involves computing total dollar gains and percentage returns. For instance, if 1,400 shares purchased at $25.44 each, with dividends of $0.58, are sold at $26.44 per share, the total dollar return is calculated as:

Capital gain per share = $26.44 - $25.44 = $1.00.

Total capital gain = 1,400 × $1.00 = $1,400.

Dividend income = 1,400 × $0.58 = $812.

Total dollar return = $1,400 + $812 = $2,212.

The percentage total return considering initial investment:

Total initial cost = 1,400 × $25.44 = $35,616.

Total return percentage = (Total dollar return / initial investment) × 100 ≈ ($2,212 / $35,616) × 100 ≈ 6.22%.

Similarly, for a stock with initial price $56, dividend $1.60, and ending price $66, the total return percentage is:

Capital gain = $66 - $56 = $10.

Dividends = $1.60.

Total dollar return = $10 + $1.60 = $11.60.

Percentage return = ($11.60 / $56) × 100 ≈ 20.71%.

Stock return analysis over five years considers annual returns of 18%, -14%, 20%, 22%, and 10%. The average annual return is calculated using:

Average return = (Sum of returns) / number of years = (18 - 14 + 20 + 22 + 10) / 5 = 56 / 5 = 11.2%.

Adjusting for inflation and risk, the average real return accounts for inflation:

Real return = [(1 + nominal return) / (1 + inflation rate)] - 1. For average nominal return ≈ 11.2%, and inflation rate 3.1%:

Real return = (1.112 / 1.031) - 1 ≈ 0.0788 or 7.88%.

The average nominal risk premium is the difference between the average nominal return and the risk-free rate (e.g., T-bill rate):

Risk premium = 11.2% - 4.4% ≈ 6.8%.

Overall, these calculations provide a comprehensive evaluation of investment growth, returns, and risk over varied financial scenarios, illustrating the importance of understanding interest compounding, discounting, and investment performance in financial decision-making.

References

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  • Fisher, I. (1930). The Theory of Interest. Macmillan.
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