time value of money - edited

8/13/2019 Time Value of Money - Edited

http://slidepdf.com/reader/full/time-value-of-money-edited 1/23

Time Value of

Money



Time Value of Money Concepts

IMPORTANT PRINCIPLE OF FINANCE:

―Money has a time value‖—money cangrow or increase over time and moneytoday is worth less than money receivedin the future

SIMPLE INTEREST: Interest earned only on the principal of theinitial investment



Time Value of Money Concepts

PRESENT VALUE:

Value of an investment or savings

amount today or at the present time Future Value: Value of an investment

or savings amount at a specified

future time BASIC EQUATION:

FV = Present value + (Present value x

Interest rate)



4

Time Value of Money Example:

Simple Interest

BASIC INFORMATION: You have

P1,000 to save or invest for one year and a

bank will pay you 8% for use of your

money. What will be the value of yoursavings after one year?

BASIC EQUATION:

FV = PV + I FV = P1,000 + (P1,000 x .08) = P1,000

+ P80 = P1,080



5

Time Value of Money Example:

Simple Interest

ALTERNATIVE BASIC EQUATION: FV = PV(1 + i)

FV = P1,000(1.08) = P1,080



6

Compounding to Determine FVs

COMPOUND INTEREST:

Earning interest on interest in

addition to interest on the principalor initial investment



7

Compounding to Determine FVs:

An Example

BASIC INFORMATION: You plan to

invest P1,000 now for two years and a

bank will pay you compound interest of

8% per year. What will be the value aftertwo years?

BASIC EQUATION:

FV = PV(1 + i)

n

FV = P1,000(1.08)2

= P1,000 x 1.1664 = P1,166.40



8

FV Problems

EXAMPLE: What is the FV of P1,000

invested now at 8% interest for 10 years?

FV = P1,000(2.1589) = P2,158.90



9

Discounting to Determine

Present Values DISCOUNTING:

An arithmetic process whereby a FV

decreases at a compound interestrate over time to reach a present

value

BASIC EQUATION: Present value = FV (1+i)-n



10

Discounting to Determine

Present Values: An Example

BASIC INFORMATION: a bank agrees

to pay you P1,000 after two years when

interest rates are compounding at 8% per

year. What is the present value of thispayment?

BASIC EQUATION:

PV = FV (1+i)-n

PV = P1,000(1.08)-2

= P1,000 x 0.8573 = P857.30



11

Present Value Problems

EXAMPLE: What is the present value of

P1,000 to be received 10 years from now if

the interest rate is 8%?

PV = FV(1+i)-n

= P1,000(1.08)-10

= P1,000(0.4632) = P463.20



12

FV of an Annuity

ANNUITY:

A series of equal payments that

occur over a number of time periods ORDINARY ANNUITY:

Exists when the equal payments

occur at the end of each time period(also referred to as a deferred

annuity)



13

FV of an Annuity

BASIC EQUATION:

FVAn = PMT (1 + i)n – 1

i

Where:

FVA = FV of ordinary annuity

PMT = periodic equal payment

r = compound interest rate, and

n = total number of periods



14

FV of an Annuity:

An Example

BASIC INFORMATION:

You plan to invest P1,000 each year

beginning next year for three years at an

8% compound interest rate. What will be

the FV of the investment?



15

FV of an Annuity:

An Example

BASIC EQUATION:

FVAn = PMT (1 + i)n - 1

i

FVA3 = P1,000 (1 +0.08)3 - 1

0.08

= P1,000(3.246)

= P3,246



16

Present Value of an Annuity

BASIC EQUATION: PVAn = PMT 1 - (1 +i)-n)

i

Where:

PVA = present value of ordinary

annuity

PMT = periodic equal payment

i = compound interest rate, and

n = total number of periods



17

Present Value of an Annuity:

An Example

BASIC INFORMATION:

You will receive P1,000 each yearbeginning next year for three years at an

8% compound interest rate. What will bethe present value of the investment?

P V l f A i



18

Present Value of an Annuity:

BASIC EQUATION:

PVAn = PMT 1 - (1 +i)-n

i

PVA3 = P1,000 1 - (1.08)-3

0.08}

= P1,000 (2.577)

= P2,577



19

APR Versus EAR

ANNUAL PERCENTAGE RATE (APR):Determined by multiplying the interest rate

charged (i) per period by the number of

periods in a year (n)

APR EQUATION:

APR = i x n

EXAMPLE:

What is the APR on a car loan that charges

1% per month?

APR = 1% x 12 months = 12%



20

APR Versus EAR (continued)

EFFECTIVE ANNUAL RATE (APR): true interest rate when compounding

occurs more frequently than annually

EAR EQUATION: EAR = (1 + i)n

- 1 EXAMPLE: What is the EAR on a credit

card loan with an 18% APR and with

monthly payments? Rate per month = 18%/12 = 1.5%

EAR = (1.015)12 - 1

= 1.1956 - 1 = 19.56%



21

Annuity Due Problems

ANNUITY DUE:

Exists when the equal periodic payments

occur at the beginning of each period

FV OF AN ANNUITY DUE (FVADn)EQUATION:

FVADn = PMT (1 + i)n – 1 (1 + i)

i



22

Learning Extension: Annuity Due

BASIC INFORMATION: You plan to invest

P1,000 each year beginning now for three

years at an 8% compound interest rate.

What will be the FV of this investment?



23

Learning Extension: Annuity Due

Problems (continued)

EQUATION:

FVADn = PMT (1 + i)n – 1 (1 + i)

i

FVAD3 = P1,000 (1.08)3 - 1) (1.08)

0.08

= P1,000[(3.246) (1.08)]

= P1,000(3.506)

= P3,506

time value of money - edited

Documents