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CHAPTER THREE

CHAPTER THREE. THE INTEREST RATE FACTOR IN FINANCING. Chapter Objectives. Present value of a single sum Future value of a single sum Present value of an annuity Future value of an annuity Calculate the effective annual yield for a series of cash flows

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CHAPTER THREE

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  1. CHAPTER THREE THE INTEREST RATE FACTOR IN FINANCING

  2. Chapter Objectives • Present value of a single sum • Future value of a single sum • Present value of an annuity • Future value of an annuity • Calculate the effective annual yield for a series of cash flows • Define what is meant by the internal rate of return

  3. Compound Interest • PV= present value • i=interest rate, discount rate, rate of return • I=dollar amount of interest earned • FV= future values • Other terms: • Compounding • Discounting

  4. Compound Interest • FV=PV (1 + i)n • When using a financial calculator: • n= number of periods • i= interest rate • PV= present value or deposit • PMT= payment • FV= future value • n, i, and PMT must correspond to the same period: • Monthly, quarterly, semi annual or yearly.

  5. The Financial Calculator • n= number of periods • i=interest rate • PV= present value, deposit, or mortgage amount • PMT= payment • FV= future value • When using the financial calculator three variables must be present in order to compute the fourth unknown. • PV or PMT must be entered as a negative

  6. Future Value of a Lump Sum • FV=PV(1+i)n • This formula demonstrates the principle of compounding, or interest on interest if we know: • 1. An initial deposit • 2. An interest rate • 3. Time period • We can compute the values at some specified time period.

  7. Present Value of a Future Sum • PV=FV 1/(1+i)n • The discounting process is the opposite of compounding • The same rules must be applied when discounting • n, i and PMT must correspond to the same period • Monthly, quarterly, semi-annually, and annually

  8. Future Value of an Annuity • FVA=P(1+i)n-1 +P(1+i)n-2 ….. + P • Ordinary annuity (end of period) • Annuity due (begin of period)

  9. Present Value of an Annuity • PVA= R 1/(1+i)1 + R 1/(1+i)2….. R 1/(1+i)n

  10. Future Value of a Single Lump Sum • Example: assume Astute investor invests $1,000 today which pays 10 percent, compounded annually. What is the expected future value of that deposit in five years? • Solution= $1,610.51

  11. Future Value of an Annuity • Example: assume Astute investor invests $1,000 at the end of each year in an investment which pays 10 percent, compounded annually. What is the expected future value of that investment in five years? • Solution= $6,105.10

  12. Annuities • Ordinary Annuity • (e.g., mortgage payment) • Annuity Due • (e.g., a monthly rental payment)

  13. Sinking Fund Payment • Example: assume Astute investor wants to accumulate $6,105.10 in five years. Assume Ms. Investor can earn 10 percent, compounded annually. How much must be invested each year to obtain the goal? • Solution= $1,000.00

  14. Present Value of a Single Lump Sum • Example: assume Astute investor has an opportunity that provides $1,610.51 at the end of five years. If Ms. Investor requires a 10 percent annual return, how much can astute pay today for this future sum? • Solution= $1,000

  15. Payment to Amortize Mortgage Loan • Example: assume Astute investor would like a mortgage loan of $100,000 at 10 percent annual interest, paid monthly, amortized over 30 years. What is the required monthly payment of principal and interest? • Solution= $877.57

  16. Remaining Loan Balance Calculation • Example: determine the remaining balance of a mortgage loan of $100,000 at 10 percent annual interest, paid monthly, amortized over 30 years at the end of year four. • The balance is the PV of the remaining payments discounted at the contract interest rate. • Solution= $97,402.22

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