Assume You Are Nearing Graduation And Have Applied For
Assume That You Are Nearing Graduation And Have Applied For a Job With
Assume that you are nearing graduation and have applied for a job with a local bank. As part of the bank's evaluation process, you have been asked to take an examination that covers several financial analysis techniques. The first section of the test addresses time value of money analysis. See how you would do by answering the following questions. Draw time lines for (a) a $2000 lump sum cash flow at the end of year 4, (b) an ordinary annuity of $1000 per year for 5 years, and (c) an uneven cash flow stream of -$450, $1000, $650, $850 and $500 at the end of years 0 through 4.
What is the future value of an initial $1000 after 5 years if it is invested in an account paying 5% annual interest? What is the present value of $1000 to be received in 4 years if the appropriate interest rate is 5%? We sometimes need to find out how long it will take a sum of money (or anything else) to grow to some specified amount. For example, if a company's sales for 2020 is $1000 and expected to grow at a rate of 10% per year, how long will it take sales to double? If you invested $10,000 in an investment account and you expect it to double in 4 years, what interest rate must it earn?
What is the future value of a 5-year ordinary annuity of $1000 if the appropriate interest rate is 5%? What is the present value of the annuity? What is the future value of $1000 after 4 years under 10% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 5%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily? Construct an amortization schedule for a $1,000, 12% annual rate loan with 4 equal installments. What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 2? Suppose on January 1 you deposit $1000 in an account that pays a nominal, or quoted, interest rate of 12%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months later? You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 6 years (72 months), and the nominal interest rate would be 10%, with interest paid monthly. What is the monthly loan payment? While Mary Corens was a student at the University of Tennessee, she borrowed $20,000 in student loans at an annual interest rate of 5%. If Mary repays $200 per year, then how long (to the nearest year) will it take her to repay the loan? Submit your answers in a Word document.
Paper For Above instruction
Assume That You Are Nearing Graduation And Have Applied For a
Financial analysis skills are critical for understanding the fundamental principles of money management, investments, and corporate finance. As a graduating student applying for a position at a local bank, demonstrating proficiency in these areas through various financial calculations and analyses is essential. This paper explores key concepts including time value of money, interest rates, annuities, loan amortization, and investment growth, providing comprehensive explanations and practical examples pertinent to banking and personal finance management.
Introduction
In the modern financial environment, understanding the time value of money (TVM) is fundamental. TVM holds that a dollar today is worth more than a dollar in the future due to its potential earning capacity. This principle underpins many financial decisions, from investing and borrowing to valuing cash flows and assessing loan options. The following sections analyze various aspects of TVM, including the construction of cash flow timelines, calculations of future and present values, growth periods, and effective interest rates, all vital for banking operations and personal financial planning.
Cash Flow Timelines
Drawing cash flow timelines helps visualize when specific cash flows occur and aids in the calculation of their present or future values. For a $2000 lump sum received at the end of year 4, the timeline shows a single cash inflow at year 4. An ordinary annuity of $1000 per year for five years involves annual cash inflows from year 1 to year 5. For uneven cash flows, each cash amount occurs at its respective year, illustrating the varying amounts over time which must be individually discounted or compounded accordingly.
Growth of an Investment Over Time
The future value (FV) of an initial investment can be 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 periods. For example, investing $1000 at 5% annually for 5 years results in FV = 1000 × (1.05)^5 ≈ $1276.28. Conversely, the present value (PV) of a future sum is PV = FV / (1 + r)^n; thus, $1000 received in 4 years at a 5% rate has a PV of approximately $821.93.
Growth Periods and Rate Calculations
Calculating how long it takes for an investment to double involves solving for n in FV = PV × (1 + r)^n. For example, if sales grow at 10% annually starting from $1000, the formula to find doubling time is n = log(2) / log(1 + 0.10) ≈ 7.27 years. Similarly, if an investment doubles in 4 years, the required interest rate r can be found using r = (FV / PV)^(1/n) - 1, which approximates to 18.92%.
Annuities and Their Values
An ordinary annuity involves equal payments made at the end of each period. The future value (FV ) of a 5-year ordinary annuity of $1000 at 5% interest is FV = P × [((1 + r)^n - 1) / r] ≈ $5525.63. The present value (PV) is PV = P × [1 - (1 + r)^-n] / r ≈ $4329.48. Under 10% interest, future values of $1000 for 4 years vary based on compounding frequency: semiannual, quarterly, monthly, and daily. For example, with quarterly compounding, FV = PV × (1 + r/4)^(4×n).
Effective Annual Rate (EAR) and Nominal Rates
The EAR converts multiple periodic rates into an annual equivalent, calculated as EAR = (1 + nominal rate / m)^m - 1, where m is the number of compounding periods per year. For a nominal rate of 5%, compounded semiannually, quarterly, monthly, or daily, the EAR increases with the number of periods: approximately 5.10%, 5.09%, 5.12%, and 5.13%, respectively. The EAR provides a more accurate measure of actual earning potential than nominal rates alone.
Loan Amortization and Schedule Construction
An amortization schedule details payments, interest expenses, and principal reductions over the life of a loan. For a $1,000 loan at 12% annual rate repaid in four equal installments, each payment can be calculated using the loan amortization formula. During Year 2, interest expense for the borrower is determined by the remaining loan balance multiplied by the interest rate. Similarly, the lender's interest income equals the interest portion earned from the borrower’s payments during that year.
Compounded Interest and Future Value
Depositing $1000 at an annual nominal rate of 12%, compounded daily, results in a future value (FV) after 9 months calculated as FV = PV × (1 + r/n)^(n × t), where n is the number of compounding periods per year, and t is time in years. This demonstrates how compounding frequency accelerates growth.
Consumer Loans and Payment Calculations
For a car loan of $10,000 amortized over 6 years with a 10% nominal annual interest rate compounded monthly, monthly payments are calculated using the standard loan payment formula. For the student loan example, with Mary repaying $200 annually at 5% interest, the repayment period can be estimated by solving for the number of periods until the balance reaches zero via amortization formulas and in iterative methods.
Conclusion
Mastering these financial analysis techniques reflects a solid understanding of core financial principles crucial for banking professionals. Applying these concepts accurately enables effective decision-making, risk assessment, and financial planning, supporting both individual and corporate financial health. As a prospective banker, possessing proficiency in time value of money calculations, loan amortizations, and understanding interest rate effects is invaluable in providing sound financial advice and services.
References
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