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The Time Value of Money

- Chapter Three

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 -- 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

- 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 todays 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

- Definition -- is the frequency that interest is

applied to the investment - Examples -- daily, monthly, or annually

Reinvesting -- How to Earn Interest on Interest

- Future-value interest factor (FVIFi,n) is a value

used as a multiplier to calculate an amounts

future value, and substitutes for the (1 i)n

part of the equation.

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

- 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

- 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 (contd)

- 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 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 (contd)

- 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

- REMEMBER -- The tables have a discrepancy due to

rounding error therefore, the calculator is more

accurate.

Compounding and the Power of Time

- In the long run, money saved now is much more

valuable than money saved later. - Dont ignore the bottom line, but also consider

the average annual return.

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

- 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

- 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

- PV FVn (PVIFi,n)
- PV the present value, in todays 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 todays value

of some future sum of money.

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

- 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

- 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

- FVn PMT (FVIFAi,n)
- FVn the future value, in todays 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 (contd)

- 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

- 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

- PVn PMT (PVIFAi,n)
- PVn the present value, in todays 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 (contd)

- 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?

- 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

- 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

- 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

- 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

- 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 todays value of an investment

received in the future

Summary (contd)

- 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 todays value of a

stream of investments received in the future

Summary (contd)

- Amortized loans loans paid in equal periodic

installments for a specific length of time - Perpetuities annuities that continue forever

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