McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

CHAPTER PLAY L I ST SONGS:

“B ang on the D rum A l l Day” by Todd

Rundgr en“A l l Wor k and No P lay” by Van Morr i son “S i x teen Tons” by Ten nessee Er n ie For d

Time Value of Money

2-2

Learning Objectives

LO 2-1 Explain what gives paper currency value and how the Federal Reserve Banks manage

its distribution.

LO 2-2 Differentiate between simple and compound interest rates and calculate annual

percentage yields and the value of paying yourself first.

LO 2-3 Calculate the future and present value of lump sums and annuities in order to

know what to put aside to meet your personal financial goals.

2-3

Money Production

Money is produced by our Government Cash is produced by the Bureau of Engraving &

Printing in D.C. and Fort Worth Coins are produced by the US mint in Philadelphia and

DenverMoney is then sent to the Federal Reserve

banks.

2-4

Power of Compounding “The most powerful force in the universe is

compound interest” ~ Albert Einstein

If Ben Franklin deposited $20 for you 250 years ago, what would its value be at 5%, 8% and 10% interest rates?

2-5

Compounding Interest

Compounding: Process whereby the value of an investment increases exponentially over time due to earning interest on interest previously earned

Annual Percentage Rate (APR): Annual rate charged for borrowing or made by investing

Annual Percentage Yield (APY): Effective yearly rate of return taking into account the effect of compounding interest

2-6

Simple Interest vs. Compound Interest

Simple Interest on $1,000 @12%Deposit of $1,000 on Jan. 1…$1,000 + (1,000 x .12) = $1,120 Resulting balance on Dec. 31

Compound Interest Quarterly on $1,000 @12%12% ÷ 4 time periods = 3% per quarter Deposit of $1,000 on Jan. 1…$1,000.00 + (1,000.00 x .03) = $1,030.00$1,030.00 + (1,030.00 x .03) = $1.060.90$1,060.90 + (1,060.90 x .03) = $1,092.73$1,092.73 + (1,092.73 x .03) = $1,125.51 Resulting balance on Dec. 31

2-7

Annual Percentage Yield (APY)

Compound Interest Quarterly on $1,000 @12%12% ÷ 4 time periods = 3% per quarter Deposit of $1,000 on Jan. 1… $1,000.00 + (1,000.00 x .03) = 1,000.00 + 30.00 = $1,030.00 $1,030.00 + (1,030.00 x .03) = 1,030.00 + 30.90 = $1,060.90 $1,060.90 + (1,060.90 x .03) = 1,060.90 + 31.83 = $1,092.73 $1,092.73 + (1,092.73 x .03) = 1,092.73 + 32.78 = $1,125.51Resulting interest yield Dec. 31... 30.00 + 30.90 + 31.83 + 32.78 = $125.51 Annual Yield

125.51/1,000 = 12.55% APY

2-8

Annual Percentage Yield (APY)

APY = (1 + r/n)n – 1

r = stated annual interest rate n = number of times compounded/year

2-9

APY Examples

The 12% rate compounded annually yields (1 + .12/1)1 – 1 =

12.00%semiannually yields (1 + .12/2)2 – 1 =

12.36%quarterly yields (1 + .12/4)4 – 1 =

12.55%monthly yields (1 + .12/12)12 – 1 =

12.68%daily yields (1 + .12/365)365 – 1 =

12.75%

2-10

Lottery Winner???

If you won the lottery would it be better to take the cash option now or choose to receive the amount in payments over your expected lifetime?

2-11

Time Value of Money

A dollar now is worth more than a dollar in the future, even after adjusting for inflation, because a dollar now can earn interest or other appreciation until the time the dollar in the future would be received.

2-12

Time Value of Money Example

Age Smart Sam Amount Deposited Wild Willie

Amount Deposited Dedicated Dave

Amount Deposited

19 $2,000.00 $2,000.00 $2,000.00 $2,000.00 20 $4,200.00 $2,000.00 $4,200.00 $2,000.00 21 $6,620.00 $2,000.00 $6,620.00 $2,000.00 22 $9,282.00 $2,000.00 $9,282.00 $2,000.00 23 $12,210.20 $2,000.00 $12,210.20 $2,000.00 24 $15,431.22 $2,000.00 $15,431.22 $2,000.00 25 $18,974.34 $2,000.00 $18,974.34 $2,000.00 26 $22,871.78 $2,000.00 $22,871.78 $2,000.00 27 $27,158.95 $2,000.00 $27,158.95 $2,000.00 28 $31,874.85 $2,000.00 $31,874.85 $2,000.00 29 $35,062.33 $2,000.00 $2,000.00 $37,062.33 $2,000.00 30 $38,568.57 $4,200.00 $2,000.00 $42,768.57 $2,000.00 31 $42,425.42 $6,620.00 $2,000.00 $49,045.42 $2,000.00

2-13

Time Value of Money Example (continued)

60 $672,998.45 $402,275.53 $2,000.00 $1,075,273.98 $2,000.00 61 $740,298.29 $444,503.09 $2,000.00 $1,184,801.38 $2,000.00 62 $814,328.12 $490,953.40 $2,000.00 $1,305,281.52 $2,000.00 63 $895,760.94 $542,048.74 $2,000.00 $1,437,809.67 $2,000.00 64 $985,337.03 $598,253.61 $2,000.00 $1,583,590.64 $2,000.00 65 $1,083,870.73 $660,078.97 $2,000.00 $1,743,949.71 $2,000.00 66 $1,192,257.81 $728,086.87 $2,000.00 $1,920,344.68 $2,000.00 67 $1,311,483.59 $802,895.56 $2,000.00 $2,114,379.14 $2,000.00 68 $1,442,631.95 $885,185.11 $2,000.00 $2,327,817.06 $2,000.00 69 $1,586,895.14 $975,703.62 $2,000.00 $2,562,598.76 $2,000.00

70 $1,745,584.65 $1,075,273.98 $2,000.00 $2,820,858.64 $2,000.00 Amount Invested

at 10% $20,000.00 $84,000.00 $104,000.00

2-14

FYI

Saving $2000 per year is only $166.67 per month or $38.46 per week or $5.48 per day.

A pack a day smoker spends $49 dollars a week, $208 dollars a month, and $2,548 a year

The average coffee drinker spends $1,100 per year

What could you give up today so you could have a million dollars in the future?

2-15

Secrets to Making Compounding Work

Pay yourself first Automatic transfer to savings and investment

accounts Transfer money on payday Treat it like a bill

Start smallIncrease the amount at least annuallyDon’t touch the money

2-16

Time Value of Money

Future Value: The projected value of an asset based on the interest rate and time in the account

Present Value: The current value of an asset to be received in the future based on the interest rate and time in the account

Lump Sum: A single, one-time payment Annuity: A series of equal payments made at

equal intervals over time (day, month, year)

2-17

Future Value (FV), Long-Hand Method

FV = PV (1 + i)n where

FV = Future value

PV = Present value

i = Interest rate

n = Number of periods

2-18

Problem

At the time of your birth your aunt deposited $10,000 for you into an account earning 5% annually. How much money will you have on your 18th birthday? How much money will you have when you turn 30? How much money will you have by the time you retire at age 65?

2-19

Future Value (FV), Long-hand Method Example:

$10,000 at Birth, Earning 5% Annually, Age 18

FV = PV (1 + i)n

FV = $10,000 (1 + 0.05)18

FV = $10,000 (1.05) 18

FV = $10,000 (2.41)

FV = $24,066.19 on your 18th birthday

2-20

FV = PV (1 + i)n

FV = $10,000 (1 + 0.05)30

FV = $10,000 (1.05)30

FV = $10,000 (4.32)FV = $43,219.42 on your 30th birthday

Future Value (FV), Long-hand Method Example:

$10,000 at Birth, Earning 5% Annually, Age 30

2-21

FV = PV (1 + i)n

FV = $10,000 (1 + 0.05)65

FV = $10,000 (1.05)65

FV = $10,000 (23.84)FV = $238,399.01 on your 65th birthday

Future Value (FV), Long-hand Method Example:

$10,000 at Birth, Earning 5% Annually, Age 65

2-22

Future Value Interest Factor (FVIF) Table Method

Future Value Interest Factor (FVIF): Factor multiplied by today’s amount to determine value of said amount at a future date

2-23

Future Value (FV), Reference Table Method Example:

$10,000 at Birth, Earning 5% Annually, Age 18

FV = PV (FVIFi,n)

FV = $10,000 (FVIF5,18)

FV = $10,000 (2.4066)FV = $24,066.00 on your 18th birthday

2-24

Future Value (FV), Reference Table Method Example:

$10,000 at Birth, Earning 5% Annually, Age 30

FV = PV (FVIFi,n)

FV = $10,000 (FVIF5,30)

FV = $10,000 (4.3219)FV = $43,219.00 on your 30th birthday

2-25

Present Value of a Lump Sum

Discounting: The reverse of compounding; finding the present value of a future amount by deducting the interest to be made

2-26

Present Value (PV), Long-Hand Method

PV = FV/(1 + i)n where

PV = Present value

FV = Future value

i = Interest rate

n = Number of time periods

2-27

Problem

You want your newborn to have $10,000 at age 18. How much would have to be deposited, assuming a 6% interest rate compounded annually (simple interest)?

2-28

Present Value (PV), Long-hand Method Example:

$10,000 in 18 Years, Earning 6% Annually

PV = FV (1 + i)n

PV = $10,000/(1 + 0.06)18

PV = $10,000/(1.06)18

PV = $10,000/(2.85)

PV = $3,503.44 to be deposited

2-29

Present Value Interest Factor (PVIF) Table Method

Present Value Interest Factor (PVIF): Factor multiplied by a future amount so as to determine the value of said amount today

2-30

Present Value (PV), Reference Table Method Example:

$10,000 in 18 Years, Earning 6% Annually

PV = FV (PVIFi,n)

PV = $10,000 (PVIF6,18)

PV = $10,000 (.3503)PV = $3,503.00 to be deposited

2-31

Future Value of an Annuity

Ordinary Annuity: Stream of equal payments that occurs at the end of a period

Annuity Due: Stream of equal payments that occurs at the beginning of a period

2-32

Future Value of an Annuity (FVA), Long-Hand Method

FVA = PMT {[(1 + i)n – 1]/i}

where

FVA = Future value of an annuity

PMT = Payment

i = Interest rate

n = Number of time periods

2-33

Problem

Your parents want to contribute to your child’s education, but instead of a lump sum payment of $3,500, they plan to contribute $500 each year for 18 years. How much money will your child have in his or her educational fund after 18 years at 6% interest?

2-34

Future Value of an Annuity (PVA), Long-hand Method Example:

$500 Payments for 18 years, Earning 6% Annually

FVA = $500{[(1 + 0.06)18 – 1]/0.06}FVA = $500{[(1.06)18 – 1]/0.06}FVA = $500[(2.85– 1)/0.06]FVA = $500(1.85/0.06)FVA = $500(30.91)FVA = $15,452.83 funded

2-35

Future Value Interest Factor of an Annuity (FVIFA)

Future Value Interest Factor of an Annuity (FVIFA): Factor multiplied by the annuity (payment) to determine the amount in the account at a future date

2-36

Future Value of an Annuity (FVA), Reference Table Method Example:

$500 Payments for 18 Years, Earning 6% Annually

FVA = PMT x FVIFA i, n

FVA = $500 x 30.906FVA = $15,453.00 funded

2-37

Calculating an Annuity Due

1. Solve for an ordinary annuity by using the formula FVA = PMT {[(1 + i)n – 1]/i}, or the FVA table.

2. Multiply it by 1 plus the interest rate (1 + i) since the payments come at the beginning of the period.

FVAd = FVA(1 + i) where

FVAd = Future value of an annuity dueFVA = Future value of an ordinary annuity i = Interest rate per period

2-38

Annuity Due from Previous Example

FVAd = FVA(1 + i)

FVAd = $15,453.00(1 + 0.06)

FVAd = $15,453.00(1.06)

FVAd = $16,308.18 funded

2-39

Present Value of an Annuity (PVA), Long-Hand Method

PVA = PMT ({1 – [1/(1 + i)n]}/i)

where

PVA = Present value of annuity

PMT = Payment

i = Interest rate per period

n = Number of periods

2-40

Problem

You want to be able to retire at age 65 with an income stream of $100,000 a year for the next 20 years. You think you will get a 5% return on your money. How much money will you need to save before you retire?

2-41

Present Value of an Annuity (PVA), Long-hand Method Example:

$100,000 Payment in 20 Years, Earning 5%

PVA = $100,000 ({1 – [1/(1 + 0.05)20]}/0.05)PVA = $100,000 ({1 – [1/(1.05)20]}/0.05)PVA = $100,000 {[1 - (1/2.65)]/0.05}PVA = $100,000 [(1 - .38)/0.05] PVA = $100,000 (.62/0.05)PVA = $100,000 (12.46)PVA = $1,246,221.03 needed in retirement savings

2-42

Present Value Interest Factor of an Annuity (PVIFA)

Present Value Interest Factor of an Annuity (PVIFA): Factor multiplied by the annuity (payment) to determine the value of the annuity today

2-43

Present Value of an Annuity (PVA), Reference Table Method Example:

$100,000 Payments in 20 Years, Earning 6%

PVA = PMT x PVIFA i, n

PVA = $100,000 x PVIFA 6, 20

PVA = $100,000 x 12.462PVA = $1,246,200.00 needed in

retirement savings

2-44

Calculating Loan Payments

PVA = PMT ({1 – [1/(1 + i)n]}/i)

where

PVA = Present value of an ordinary annuity

PMT = Payment

i = Interest rate per period

n = Number of periods

2-45

Problem

If you are financing $15,000 at 6% interest for three years, making annual payments, you know the following:

PVA = 15,000

i = .06

n = 3

2-46

Long-Hand Method

Annual Loan Payment Calculation

15,000 = PMT ({1 – [1/(1 + .06)3]}/.06)15,000 = PMT {[1 – (1/1.063)]/.06}15,000 = PMT {[1 – (1/1.19)]/.06}15,000 = PMT [(1 – .84)/.06]15,000 = PMT (.16/.06)15,000 = PMT (2.67301)Divide both sides by 2.67301 and your

answer is:$5,611.65 = PMT

2-47

PVA = PMT (PVIFAi,n)

15,000 = PMT (2.673)

5,611.67 = PMT

Reference Table Method

Annual Loan Payment Calculation

2-48

Monthly Payments

To determine your monthly payments, divide your interest rate by 12. Your number of payments is now 36. For the above example, we would have the following:PVA = 15,000i = .06/12 = 0.005n = 36PMT = ?

2-49

Using the formula, your equation would be as follows

15,000 = PMT ({1 – [1/(1 + .005)36]}/.005)15,000 = PMT {[1 – (1/1.005)36]/.005}15,000 = PMT {[1 – (1/1.19668)]/.005}15,000 = PMT [(1 –.84)/.005]15,000 = PMT (.16/.005)15,000 = PMT (32.8710)456.33 = PMT

Long-Hand Method

Monthly Loan Payment Calculation

2-50

Extrapolating, you would find PVIFA.5, 36 equals 32.871

PVA = PMT (PVIFAi,n)15,000 = PMT (32.871)456.33 = PMT

Reference Table Method

Monthly Loan Payment Calculation

2-51

Learn

LO 2-1 Explain what gives paper currency value and how the Federal Reserve Banks manage its distribution.

LO 2-2 Differentiate between simple and compound interest rates and calculate annual percentage yields and the value of paying

yourself first.LO 2-3 Calculate the future and present value

of lump sums and annuities in order to know what to put aside to meet your financial goals.

2-52

Plan & Act

Assess the cost of your goals from Chapter 1 (Worksheet 2.1).

Review your options for designating current savings to a specific future goal and calculate how much money you need to deposit annually to support that long-term goal (Worksheet 2.2).

Calculate how much you need to set aside in savings each your, starting now, to reach your retirement goal (Worksheet 2.3).

Consider starting a ‘Dedicated Dave’ automatic deposit account by putting $5 per day into savings.

2-53

Evaluate

Open the online GoalTracker after completing Worksheet 2.1 and record the estimated costs and savings plans of your SMART goals.

Assess how you are achieving your goals.

2-54

Continuing Case: Investment Options

Housemate Goal

Leigh Art teacher, works part-time at co-op for the discount, bikes to work, is a vegetarian, gardens, has egg-laying backyard hens

Backpack through Europe for a summer in 5 years

Blake Junior, business student, expected to take on family business, wants to work on Wall Street

Compete in Hawaiian Iron Man in 5 years

Nicole Freshman, pre-nursing for the moment, somewhat spoiled

Graduate in 4 years

Karri 5th year student, Communications major; Loves shoes, high fashion, chocolate, wine, and the Big Apple

Anchor the evening news for a local television network

Peter Sous chef, internship in Tokyo, would love someday to go back and visit, wants to summit all the CO high peaks

Open his own sushi restaurant in 3 years

Brett  2nd year med student, focused on emergency medicine, interested in volunteering for Doctors without Borders

Complete med school and residency with little/no debt

Jen Freshman, Community College, undecided major, very social, fastest texter in high school graduating class

Pick a major, transfer to the university after 2 years, graduate in 4 years

Jack Newly graduated in General Studies, part-time bartender, in to paintball

Not move back with parents and decide on a career