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Time is Money: Time is Money: Personal Finance Applications Personal Finance Applications
of the Time Value of Moneyof the Time Value of Money
Barbara O’Neill, Ph.D, CFP
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Time : A Financial Management Tool
• “A penny saved is a penny earned”
• “Time is money”
• “I’m on the clock”
• “I’m buying myself some time”
• “Timing is everything”• Albert Einstein: quote about compound interest
Too many young people don’t appreciate the awesome power of the time value of money!!!
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Time Reduces Investment Volatility
Source: Ibbotson Associates
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So What Exactly Is The Time Value of Money? (Review)
Key message of remainder of class:
Compound interest can be...
• Your worst enemy (credit card debt)
• Your best friend (5+ decades of compound interest)
The choice is up to you!
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Ways to Calculate TV of Money
• Mathematically
• Financial calculator (e.g. TI-BA35)
• Computer spreadsheets with formulas
– (e.g., Microsoft Excel)
• TV of money interest factor tables
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Let’s Review
• Future value of a lump sum– Example: Value of $10,000 gift today in 20
years– 8% i, N =20, FVF =4.6610 ($46,610)
• Present value of a lump sum– Example: Value of a $10,000 gift in 20 years
today– 8%i, N =20, PVF =.2145 ($2,145)
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More Review: What Is An Annuity?
Two types of annuities (according to timing of receipt or payment of $)
• Ordinary Annuity: payment at end of period– Examples: bank account interest, stock
dividends, car note, mortgage
• Annuity Due: payment at start of period– Examples: insurance premiums, leases
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Which Type of Annuity is Better If You’re an Investor?
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Annuity Due
• The sooner a dollar is received, the sooner the compounding process begins
• FV and PV of an annuity due are always greater than FV and PV of ordinary annuity
– Common Example: Funding an IRA on Jan. 1 versus April 15 of the following year
• Compound interest magnifies the difference in returns over time
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Key Variables in TV of Money Problems
• N- Number of compounding periods
• % i- Interest rate (for compounding FV or discounting PV)
• PV
• FV• For annuity calculations, periodic payment or receipt amount
– Enter 3 known variables; solve for the 4th (unknown) variable
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Problem #1
Your first “real” job pays $32,000 a year to start. How much will you need to be earning in 20 years to maintain the same purchasing power if inflation averages
3%?
4%?
5%?
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Problem #2
• Your grandparents (age 60 and 62) are about to retire next month with a monthly income of $2,000. Assuming an annual inflation rate of 4%, how much will they need in 10 years to equal the purchasing power of $2,000 today?
20 years?
30 years?
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What can your grandparents do to prevent inflation from eroding
their purchasing power?
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Problem #3
Your rich uncle has promised to give you $25,000. The only “catch” is that you must graduate from college and get a “real job” before he gives it to you. Let’s assume that’s in 4 years. What is the value of his gift today if his money is earning
5%?
7%
10%
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Problem #4
Kevin is 19 and wants to have $10,000 saved by the time he’s 25. Thanks to a generous gift from his grandparents, he currently has $6,500 invested in a bond paying 5%. If he makes no further deposits, will he reach his goal?
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How could Kevin reach (or exceed) his goal?
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Problem #5
Heather starts a Roth IRA at age 22. She plans to contribute $3,000 at the end of each year year for 45 years until age 67. How much will she have if her IRA investments earn 4% ?
7% ?
9% ?
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$3,000 a Year is About $60 a Week of Savings
How can Heather “find” $60 a week to invest in her Roth IRA?
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Problem #6
Wendy and Sal just got married and want to save $15,000 for a down payment and closing costs on their first house. They intend to save $500 per month in CDs averaging a 4% annual return. How long will it take them to reach their goal?
Hints: Use a financial calculator…The answer is less than 5 years!
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Problem #7
You quit smoking a pack a day of cigarettes and save $2,550 a year (savings of $7 per pack per day). You are 20. How much would you have if you invested the money in a stock index fund averaging a 10% return and don’t touch it until age 55?
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Problem #8
Lucky you…you won the NJ lottery. You have a choice between receiving $1,000,000 as an annuity of $50,000 a year over 20 years or taking $500,000 as a lump sum payment today. Ignoring taxes for the moment and, assuming a discount rate of 6%, which option is the best deal?
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Problem #9
You want a $1 million dollars when you retire and will average a 10% return. How much do you need to save per year if you have…
• 40 years to save?
• 30 years to save?
• 20 years to save?
• 10 years to save?
What do these results tell you?
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Problem #10
• Your grandparents, both age 62, have a retirement fund of $100,000 saved to supplement their pension and Social Security. Assuming an average annual interest rate of 7%, how long will the fund last if they withdraw $750 per month? What would you advise them to do?
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Two Take-Home Messages:
1. For every decade that you delay saving, the required investment triples (approx.)
2. Compound interest is NOT retroactive!!!
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The Millionaire Game:
A Perfect Metaphor For Compound Interest
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A: Answer A
C: Answer C
B: Answer B
D: Answer D
50:50
151413121110987654321
$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100
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YOU WIN $1 MILLION DOLLARS!