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Answer & Explanation:Unit 6 Discussion Write a 1 page paper, double spaced that summarizes the Seminar and what you learned.  Seminar Attached.unit_6.pptx
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Chapter 4 – Annuities and Loans
ANNUITIES
Unit 6- Chapter 4
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Chapter 4 – Annuities and Loans
Definition: Annuity
❖Annuity
• A stream of equal periodic cash flows
• Series of equal payments made at equal intervals
• Can be inflows or outflows
❖Ordinary annuity
• An annuity for which the payments occur at the end of each period
❖Annuity due
• An annuity for which the payments occur at the beginning of each period
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Chapter 4 – Annuities and Loans
Future Value of an Ordinary Annuity
❖Future balance after 3 years of 3 annual $100
deposits
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Chapter 4 – Annuities and Loans
Future Value of an Ordinary Annuity
Future balance after 3 years of 3 annual $100
deposits (10% rate)
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Chapter 4 – Annuities and Loans
Future Value of an Ordinary Annuity: Using
Excel
Formulas
Insert Function
FV
Rate: .10
Nper: 3
PMT: -100
PV: 0
FV= $331.00
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Chapter 4 – Annuities and Loans
Future Value of an Ordinary Annuity
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Chapter 4 – Annuities and Loans
Future Value of an Ordinary Annuity
Use Excel for Previous Example:
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Chapter 4 – Annuities and Loans
Future Value of an Ordinary Annuity
Use Excel and calculate the PMT
= (7,233.96)
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Chapter 4 – Annuities and Loans
Present Value of Streams of Payments
❖Present value of an ordinary annuity
• What is the present value of $100 per year paid at the end of each year
at 10% interest?
10 Chapter 4 – Annuities and Loans
Present Value of Ordinary Annuity: Using Excel
Formulas
Insert Function
PV
Rate: .10
Nper: 4
PMT: -100
FV: 0
PV= $316.99
11 Chapter 4 – Annuities and Loans
FV of Annuity Due: Using Excel
Future balance after 7 years of 2,000 annuity payments that grow at 8%
annually, payments made at the beginning of each year?
Formulas
Insert Function
FV
Rate: .08
Nper: 7
PMT: -2000
PV: 0
Type: 1
FV= $19,273.26
12 Chapter 4 – Annuities and Loans
PV of Annuity Due: Excel
You won the lottery and the prize is $100 paid at the beginning of each year for the
next 4 years. What is the PV of the annuity if the interest rate is 10%?
Formulas
Insert Function
PV
Rate: .10
Nper: 4
PMT: -100
FV: 0
Type: 1
PV= $348.69
13 Chapter 4 – Annuities and Loans
Perpetuity
If the annuity continues forever, it is called perpetuity.
The word perpetuity comes form the word perpetual,
which means continual or everlasting.
Equation for PV of a perpetuity:
PV = PMT/ i
14 Chapter 4 – Annuities and Loans
PV of a Perpetuity
Determine the PV of the dividends paid by a share of
preferred stock. We know that the stock promises to
pay the holder an annual $100 dividend forever, and we
assume a 10% interest rate.
PV= $100/.10= $1,000
As investors, we would be willing to pay no more than
$1,000 for a share of this stock.
15 Chapter 4 – Annuities and Loans
Example
You are trying to decide how much money you will need at
retirement. You expect to retire at age 65. You hope to travel
extensively while you are healthy enough. To finance your
travels, you think you will need income of $242,000 per year. You
will make the first withdrawal on your 66th birthday. You expect
to travel for 12 years. Once you stop traveling, you will need
$227,000 income per year. You expect to live another 7 years at
that income level. Your expected rate of return is 4%. How much
will you need at retirement?
16 Chapter 4 – Annuities and Loans
Answer- Multi Step
Step 1: Find PV of traveling years
Rate: .04
Nper: 12
PMT: -242000
FV: 0
PV= $2,271,187.85
17 Chapter 4 – Annuities and Loans
Step 2
Step 2: Find PV of Non traveling Years (retirement year
13)
Rate: .04
Nper: 7
PMT: -227000
FV: 0
PV= $1,362,466.41
18 Chapter 4 – Annuities and Loans
Step 3
Step 3: Find PV of Non traveling Years (retirement years 1-12)
Rate: .04
Nper: 12
PMT: 0
FV: 1362466.41
PV= ($850,992.50)
Answer: Add $850,992.50 + $2,271,187.85= $3,122,180.30
19 Chapter 4 – Annuities and Loans
Examples
Tony plans to deposit $1,000 at the end of each of the
next 3 years. If his funds earn 5% annually, how much
will he have at the end of the 3 years?
20 Chapter 4 – Annuities and Loans
Answer
$3,152.50
21 Chapter 4 – Annuities and Loans
Examples
You are 30 years old and you want to retire at age 60
with 1.5 million. You are going to make equal annual
deposits into your savings account at the end of each
year in order to save up this money. Your savings
account pays 8% interest. What amount must you
deposit each year?
22 Chapter 4 – Annuities and Loans
Answer
$13,241.15
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