Question 1: After Placing $13,000 In A Savings Account Payin

Question 1after Placing 13000 In A Savings Account Paying Annual Co

After placing $13,000 in a savings account paying annual compound interest of 3%, Leona will accumulate what amount if she leaves the money in the bank for 4 years?

You have just introduced "must have" headphones for the iPod. Sales of the product are expected to be 20,000 units this year and are expected to increase by 16% annually in the future. What are the expected sales in each of the next three years? If the 20,000 units were expected to increase by 18% a year, what are the expected sales next year for this product?

What is the present value of a $650 perpetuity discounted back to the present at 10%? What is the present value of the perpetuity?

What is the present value of a perpetual stream of cash flow that pays $80,000 at the end of one year and grows at a rate of 5% indefinitely? The rate of interest used to discount the cash flows is 10%. What is the present value of the growing perpetuity?

Paper For Above instruction

In this paper, we will address several financial and business analysis questions, including compound interest calculations, sales forecasts based on growth rates, and valuation of perpetuities. These topics are fundamental in personal finance, investment analysis, and business planning, providing insight into how money and sales grow over time and how to assess the present worth of future cash flows.

Compound Interest Calculation

Leona’s investment in a savings account earning 3% annual compound interest over 4 years can be calculated using the formula for compound interest:

Future Value (FV) = PV × (1 + r)^t

Where PV = $13,000, r = 0.03, and t = 4 years. Substituting the values:

FV = 13,000 × (1 + 0.03)^4 = 13,000 × 1.12550881 ≈ $14,632.61

Therefore, after 4 years, Leona will have approximately $14,632.61 in her savings account.

Sales Forecasting with Growth Rates

Starting with initial sales of 20,000 units, expected sales over the next three years at a 16% annual growth rate are calculated as follows:

  • Year 1: 20,000 × (1 + 0.16) = 20,000 × 1.16 = 23,200 units
  • Year 2: 23,200 × 1.16 = 26,912 units
  • Year 3: 26,912 × 1.16 ≈ 31,207.52 units

Similarly, if the sales increase by 18% annually, expected sales next year would be:

20,000 × (1 + 0.18) = 20,000 × 1.18 = 23,600 units

This demonstrates how slight changes in growth rate affect future sales projections, important for planning marketing strategies and inventory management.

Valuation of Perpetuities

Perpetuity Discounted at 10%

The present value of a perpetuity paying $650 annually can be calculated with the formula:

PV = Payment / discount rate = $650 / 0.10 = $6,500

This value represents the worth of receiving $650 every year indefinitely, assuming a 10% discount rate.

Growing Perpetuity

The present value of a perpetuity that starts with a payment of $80,000 at the end of one year and grows at 5% annually, discounted at 10%, is calculated using the following formula:

PV = Payment / (discount rate - growth rate) = $80,000 / (0.10 - 0.05) = $80,000 / 0.05 = $1,600,000

This formula applies when the cash flows grow at a constant rate forever, providing a valuation tool for businesses with increasing cash flows.

Conclusion

Understanding the mechanics of compound interest, sales growth projections, and perpetuity valuation are crucial skills in finance and business management. These calculations provide essential insights into investment growth, sales forecasting, and firm valuation. Accurate application of formulas ensures better financial decision-making and strategic planning, whether assessing savings growth, forecasting future sales, or valuing perpetual income streams.

References

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