Determine The Present Value If $5,000 Is Received In T

Determine The Present Values If 5000 Is Received In T

Chapter 9: P6. Determine the present values if $5,000 is received in the future (i.e., at the end of each indicated time period) in each of the following situations: 5 percent for ten years; 7 percent for seven years; 9 percent for four years. P9. Assume you are planning to invest $5,000 each year for six years and will earn 10 percent per year. Determine the future value of this annuity if your first $5,000 is invested at the end of the first year. P10. Determine the present value now of an investment of $3,000 made one year from now and an additional $3,000 made two years from now if the annual discount rate is 4 percent. P11. What is the present value of a loan that calls for the payment of $500 per year for six years if the discount rate is 10 percent and the first payment will be made one year from now? How would your answer change if the $500 per year occurred for ten years? P12. Determine the annual payment on a $500,000, 12 percent business loan from a commercial bank that is to be amortized over a five-year period. P13. Determine the annual payment on a $15,000 loan that is to be amortized over a four-year period and carries a 10 percent interest rate. Also prepare a loan amortization schedule for this loan. P15. Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. At what amount could this loan be sold for to another bank if loans of similar quality carried an 8.5 percent interest rate? That is, what would be the present value of this loan? Now, if interest rates on other similar-quality loans are 10 percent, what would be the present value of this loan? What would be the present value of the loan if the interest rate is 8 percent on similar-quality loans?

Paper For Above instruction

Understanding the concept of present value is fundamental in financial decision-making, as it allows investors and financial managers to determine the current worth of a future sum of money or stream of cash flows given a specified rate of return. This paper explores various scenarios involving present value and future value calculations to illustrate their applications in real-world financial contexts.

Firstly, calculating the present value of $5,000 received at different future periods depends on the discount rate and the period in question. Using the formula PV = FV / (1 + r)^t, where PV is the present value, FV is the future value, r is the discount rate, and t is the time in years, we find that at 5% for ten years, the present value is approximately $3,105.75. At 7% over seven years, it is around $3,202.88; and at 9% over four years, it is about $3,258.65. These calculations demonstrate how higher discount rates and longer periods reduce present value, reflecting the opportunity cost of capital and time value of money.

Secondly, the future value of an annuity where $5,000 is invested annually for six years at 10% interest can be computed using the future value of an ordinary annuity formula: FV = P * [(1 + r)^t - 1] / r. Substituting P = 5,000, r = 0.10, and t = 6 yields a future value of approximately $36,424.45. This accumulation reflects the power of compound interest over multiple periods, particularly when consistent contributions are made the end of each period.

Next, the present value of two future payments of $3,000 each made one and two years from now, discounted at 4%, can be calculated by summing the individual present values: PV = 3,000 / (1.04)^1 + 3,000 / (1.04)^2, resulting in a total present value of approximately $5,571.94. This emphasizes how discount rates diminish the current worth of future cash flows.

Further, evaluating a loan's present value involves discounting the series of payments, such as $500 annually over six or ten years, at a 10% discount rate. The present value of an annuity of $500 over six years is roughly $2,595.64, while extending to ten years increases the PV to approximately $3,790.78. Such calculations are crucial in assessing loan pricing and investment returns.

Amortization of loans, such as a $500,000 loan at 12% interest over five years, involves equal annual payments that cover both principal and interest. Calculations show that the annual payment would be approximately $132,073, which includes interest and principal repayment components. Similarly, a $15,000 loan at 10% over four years results in an annual payment of about $4,017. Furthermore, amortization schedules break down each payment into interest and principal components over the loan term, offering transparency and aiding borrower understanding.

The valuation of loans based on their interest payments and remaining principal can be understood through present value calculations. For a loan with an annual interest payment of $85 and a principal of $1,000 paid at the end of eight years, its current value depends on the prevailing market interest rate. If the market rate is 8.5%, the present value would be higher compared to a 10% rate, demonstrating the inverse relationship between market interest rates and loan valuation. A shift in interest rates significantly influences the loan's market value, with lower rates increasing valuation and higher rates decreasing it.

In conclusion, the various scenarios discussed—ranging from simple present value calculations to complex loan amortizations—highlight the critical role of time value of money principles in financial analysis. Mastery of present and future value computations enables better-informed financial decisions, optimal investment strategies, and effective risk management across personal finance, corporate finance, and banking sectors.

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