110ch03

The Time Value of Money: 

The Time Value of Money Chapter Three

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: 

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.

Future Value Equation: 

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.

Compounding Period: 

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

Reinvesting -- How to Earn Interest on Interest: 

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.

The Future Value of a Wedding: 

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

The Rule of 72: 

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

Compound Interest With Nonannual Periods: 

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.

Compound Interest With Nonannual Periods (cont’d): 

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

The Time Value of a Financial Calculator: 

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

The Time Value of a Financial Calculator (cont’d): 

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.

Tables Versus Calculator : 

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

Compounding and the Power of Time: 

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.

The Power of Time in Compounding Over 35 Years: 

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.

The Importance of the Interest Rate in Compounding: 

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.

Present Value: 

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.

Present Value Equation: 

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.

Calculating Present Value for the “Prodigal Son”: 

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

Annuities: 

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.

Compound Annuities: 

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

Future Value of an Annuity Equation: 

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

Future Value of an Annuity Equation (cont’d): 

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.

Calculating the Future Value of an Annuity: An IRA: 

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

Present Value of an Annuity Equation: 

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

Present Value of an Annuity Equation (cont’d): 

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.

Calculating Present Value of an Annuity: Now or Wait?: 

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

Amortized Loans: 

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

Buying a Car With Four Easy Annual Installments: 

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

Perpetuities: 

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

Summary: 

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

Summary (cont’d): 

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

Summary (cont’d): 

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