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Chapter 3

Chapter 3. Understanding The Time Value of Money. Time Value of Money. A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest, the faster the interest can earn interest. Interest and Compound Interest.

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Chapter 3

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  1. Chapter 3 Understanding The Time Value of Money

  2. Time Value of Money • A dollar received today is worth more than a dollar received in the future. • The sooner your money can earn interest, the faster the interest can earn interest.

  3. Interest and Compound Interest • Interest -- is the return you receive for investing your money. • Compound interest -- is the interest that your investment earns on the interest that your investment previously earned.

  4. Future Value Equation • FVn = PV(1 + i)n • FV = the future value of the investment at the end of n year • i = the annual interest (or discount) rate • PV = the present value, in today’s dollars, of a sum of money • This equation is used to determine the value of an investment at some point in the future.

  5. Compounding Period • Definition -- is the frequency that interest is applied to the investment • Examples -- daily, monthly, or annually

  6. Reinvesting -- How to Earn Interest on Interest • Future-value interest factor (FVIFi,n) is a value used as a multiplier to calculate an amount’s future value, and substitutes for the (1 + i)n part of the equation.

  7. The Future Value of a Wedding In 1998 the average wedding cost $19,104. Assuming 4% inflation, what will it cost in 2028? FVn = PV (FVIFi,n) FVn = PV (1 + i)n FV30 = PV (1 + 0.04)30 FV30 = $19,104 (3.243) FV30 = $61,954.27

  8. The Rule of 72 • Estimates how many years an investment will take to double in value • Number of years to double = 72 / annual compound growth rate • Example -- 72 / 8 = 9 therefore, it will take 9 years for an investment to double in value if it earns 8% annually

  9. Compound Interest With Nonannual Periods The length of the compounding period and the effective annual interest rate are inversely related; therefore, the shorter the compounding period, the quicker the investment grows.

  10. Compound Interest With Nonannual Periods (cont’d) • Effective annual interest rate = amount of annual interest earned amount of money invested • Examples -- daily, weekly, monthly, and semi-annually

  11. The Time Value of a Financial Calculator • The TI BAII Plus financial calculator keys • N = stores the total number of payments • I/Y = stores the interest or discount rate • PV = stores the present value • FV = stores the future value • PMT = stores the dollar amount of each annuity payment • CPT = is the compute key

  12. The Time Value of a Financial Calculator (cont’d) • Step 1 -- input the values of the known variables. • Step 2 -- calculate the value of the remaining unknown variable. • Note: be sure to set your calculator to “end of year” and “one payment per year” modes unless otherwise directed.

  13. Tables Versus Calculator • REMEMBER -- The tables have a discrepancy due to rounding error; therefore, the calculator is more accurate.

  14. Compounding and the Power of Time • In the long run, money saved now is much more valuable than money saved later. • Don’t ignore the bottom line, but also consider the average annual return.

  15. The Power of Time in Compounding Over 35 Years • Selma contributed $2,000 per year in years 1 – 10, or 10 years. • Patty contributed $2,000 per year in years 11 – 35, or 25 years. • Both earned 8% average annual return.

  16. The Importance of the Interest Rate in Compounding • From 1926-1998 the compound growth rate of stocks was approximately 11.2%, whereas long-term corporate bonds only returned 5.8%. • The “Daily Double” -- states that you are earning a 100% return compounded on a daily basis.

  17. Present Value • Is also know as the discount rate, or the interest rate used to bring future dollars back to the present. • Present-value interest factor (PVIFi,n) is a value used to calculate the present value of a given amount.

  18. Present Value Equation • PV = FVn (PVIFi,n) • PV = the present value, in today’s dollars, of a sum of money • FVn = the future value of the investment at the end of n years • PVIFi,n = the present value interest factor • This equation is used to determine today’s value of some future sum of money.

  19. Calculating Present Value for the “Prodigal Son” If promised $500,000 in 40 years, assuming 6% interest, what is the value today? PV = FVn (PVIFi,n) PV = $500,000 (PVIF6%, 40 yr) PV = $500,000 (.097) PV = $48,500

  20. Annuities • Definition -- a series of equal dollar payments coming at the end of a certain time period for a specified number of time periods. • Examples -- life insurance benefits, lottery payments, retirement payments.

  21. Compound Annuities • Definition -- depositing an equal sum of money at the end of each time period for a certain number of periods and allowing the money to grow • Example -- saving $50 a month to buy a new stereo two years in the future • By allowing the money to gain interest and compound interest, the first $50, at the end of two years is worth $50 (1 + 0.08)2 = $58.32

  22. Future Value of an Annuity Equation • FVn = PMT (FVIFAi,n) • FVn = the future value, in today’s dollars, of a sum of money • PMT = the payment made at the end of each time period • FVIFAi,n = the future-value interest factor for an annuity

  23. Future Value of an Annuity Equation (cont’d) • This equation is used to determine the future value of a stream of payments invested in the present, such as the value of your 401(k) contributions.

  24. Calculating the Future Value of an Annuity: An IRA Assuming $2000 annual contributions with 9% return, how much will an IRA be worth in 30 years? FVn = PMT (FVIFA i, n) FV30 = $2000 (FVIFA 9%,30 yr) FV30 = $2000 (136.305) FV30 = $272,610

  25. Present Value of an Annuity Equation • PVn = PMT (PVIFAi,n) • PVn = the present value, in today’s dollars, of a sum of money • PMT = the payment to be made at the end of each time period • PVIFAi,n = the present-value interest factor for an annuity

  26. Present Value of an Annuity Equation (cont’d) • This equation is used to determine the present value of a future stream of payments, such as your pension fund or insurance benefits.

  27. Calculating Present Value of an Annuity: Now or Wait? What is the present value of the 25 annual payments of $50,000 offered to the soon-to-be ex-wife, assuming a 5% discount rate? PV = PMT (PVIFA i,n) PV = $50,000 (PVIFA 5%, 25) PV = $50,000 (14.094) PV = $704,700

  28. Amortized Loans • Definition -- loans that are repaid in equal periodic installments • With an amortized loan the interest payment declines as your outstanding principal declines; therefore, with each payment you will be paying an increasing amount towards the principal of the loan. • Examples -- car loans or home mortgages

  29. Buying a Car With Four Easy Annual Installments What are the annual payments to repay $6,000 at 15% interest? PV = PMT(PVIFA i%,n yr) $6,000 = PMT (PVIFA 15%, 4 yr) $6,000 = PMT (2.855) $2,101.58 = PMT

  30. Perpetuities • Definition – an annuity that lasts forever • PV = PP / i • PV = the present value of the perpetuity • PP = the annual dollar amount provided by the perpetuity • i = the annual interest (or discount) rate

  31. Summary • Future value – the value, in the future, of a current investment • Rule of 72 – estimates how long your investment will take to double at a given rate of return • Present value – today’s value of an investment received in the future

  32. Summary (cont’d) • Annuity – a periodic series of equal payments for a specific length of time • Future value of an annuity – the value, in the future, of a current stream of investments • Present value of an annuity – today’s value of a stream of investments received in the future

  33. Summary (cont’d) • Amortized loans – loans paid in equal periodic installments for a specific length of time • Perpetuities – annuities that continue forever

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