presentation 3
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Petroleum Project Economics Econ210D
Presentation 3
Interest and Time Value of MoneyWeek 3
1
• Interest remains constant each year.
• Interest is not reinvested
• Interest is calculated by the formula.
2
Simple Interest
nrPI
where: I = Interest, P = Principal, r = interest,
n = number of years.Interest and Time Value of Money
Week 3
• Interest is based on principal plus reinvested interest from
previous years
• Interest increase each successive year
3
Compound Interest
nrPA 1
where: P = Principal, r = interest, n =
number of years, A = Principal + Interest, Interest and Time Value of Money
Week 3
4
Future and Present Value
• Future Value – the value at some point in the future of a single cash flow or a series of cash flows in the future.
• Present Value – the value today of a single cash flow or a series of cash flows in the future
• Values change over time due to interest
• Interest is based on compound interestInterest and Time Value of Money
Week 3
5
where:F = Future valueI = Investment/Principalr = rate of interest (for each time period)n = number of time periods.
Future Value
nrIF 1
Interest and Time Value of Money Week 3
6
Present Value
nr
IP1
where:P = Present valueI = Investment/Principalr = rate of interest (for each time period)n = number of time periods.
Interest and Time Value of Money Week 3
7
Future Value of a Single Cash Flow
An investor deposits $100 into an account
which offers 12% p.a. compound interest.
What is the value of the investment at the
end of 3 years?
Interest and Time Value of Money Week 3
8
Present Value of a Single Cash Flow
An investor is supposed to receive $100 in
3 years time. If the rate of compound
interest is 12% p.a. what is the present
value of the amount?
Interest and Time Value of Money Week 3
9
Annuities – Series of Cash flows
• An annuity is a series of equal payments at evenly spaced intervals
• The payments occur at the beginning of each period for an annuity due while they occur at the end of each period for an ordinary annuity
• Interest is earned on amounts paid
Interest and Time Value of Money Week 3
10
Annuity Due and an Ordinary Annuity – over 3 years
• Annuity Due
• Ordinary Annuity
Jan 1st 2009
$100 $100 $100
$100$100 $100
Jan 1st 2009
Jan 1st 2010 Jan 1st 2011 Dec 31st 2011
Dec 31st 2009 Dec 31st 2010 Dec 31st 2011
Interest and Time Value of Money Week 3
11
At the beginning of each year an
investor deposits $100 into an account
which offers 12% p.a. compund
interest. What is the value of the
investment at the end of 3 years?
Future Value of an Annuity Due
Interest and Time Value of Money Week 3
12
Future Value of an Annuity Due
Time Year Amount Workings Future Value
Jan 1st 2009 0 $100 $140
Jan 1st 2010 1 $100 $125
Jan 1st 2011 2 $100 $112
Dec 31st 2011 3 $0 $0
Total $300 $378
Interest and Time Value of Money Week 3
13
Future Value of an Annuity Due
$0
$20
$40
$60
$80
$100
$120
$140
$160
Amount
Future Value
Amount $100 $100 $100 $0
Future Value $140 $125 $112 $0
Jan 1st 2009 Jan 1st 2010 Jan 1st 2011 Dec 31st 2012
Interest and Time Value of Money Week 3
14
Future Value of an Annuity Due using Formula
where
• I = periodic investment
• r = interest rate per period
• n = number of periods
111 1
r
rIFVA
n
DUE
Interest and Time Value of Money Week 3
15
At the end of each year an investor
deposits $100 into an account which
offers 12% p.a. compound interest.
What is the value of the investment at
the end of 3 years?
Future Value of an Ordinary Annuity
Interest and Time Value of Money Week 3
16
Future Value of an Ordinary Annuity
Time Year Amount Workings Future Value
Jan 1st 2009 0 $0 $0
Dec 31st 2009 1 $100 $125
Dec 31st 2010 2 $100 $112
Dec 31st 2011 3 $100 $100
Total $300 $337
Interest and Time Value of Money Week 3
17
Future Value of an Ordinary Annuity
$0
$20
$40
$60
$80
$100
$120
$140
Amount
Future Value
Amount $0 $100 $100 $100
Future Value $0 $125 $112 $100
Jan 1st 2009 Dec 31st 2009 Dec 31st 2010 Dec 31st 2011
Interest and Time Value of Money Week 3
18
Future Value of an Ordinary Annuity using Formula
where
• I = periodic investment
• r = interest rate per period
• n = number of periods
r
rIFVA
n
ORDINARY
11
Interest and Time Value of Money Week 3
19
At the beginning of each year an
investor deposits $10,000 into an
account which offers 10% p.a.
compound interest. What is the value of
the investment at the end of 4 years?
Question 1
Interest and Time Value of Money Week 3
20
At the end of each year an investor
deposits $2,000 into an account
which offers 2% p.a. compound
interest. What is the value of the
investment at the end of 5 years?
Question 2
Interest and Time Value of Money Week 3
21
At the end of each quarter an investor
deposits $400 into an account which
offers 12% p.a. compound interest.
What is the value of the investment at
the end of 1 year?
Question 3
Interest and Time Value of Money Week 3
22
At the beginning of each month an
investor deposits $100 into an account
which offers 12% p.a. compound
interest. What is the value of the
investment at the end of 6 months?
Question 4
Interest and Time Value of Money Week 3
23
At the beginning of each year an
investor deposits $100 into an account
which offers 12% p.a. compund
interest. What is the present value of
the investment?
Present Value of an Annuity Due
Interest and Time Value of Money Week 3
24
Present Value of an Annuity Due
Time Year Amount Workings Present Value
Jan 1st 2009 0 $100 $100
Jan 1st 2010 1 $100 $89
Jan 1st 2011 2 $100 $80
Dec 31st 2011 3 $0 $0
Total $300 $269
Interest and Time Value of Money Week 3
25
Present Value of an Annuity Due
$0
$20
$40
$60
$80
$100
$120
Amount
PresentValue
Amount $100 $100 $100 $0
Present Value $100 $89 $80 $0
Jan 1st 2009 Jan 1st 2010 Jan 1st 2011 Dec 31st 2012
Interest and Time Value of Money Week 3
26
Present Value of an Annuity Due Using the formula
11
11 1
rr
IPVAn
DUE
where
• I = periodic investment
• r = interest rate per period
• n = number of periodsInterest and Time Value of Money
Week 3
27
At the end of each year for 3 years an
investor deposits $100 into an account
which offers 12% p.a. compound
interest. What is the present value of the
investment?
Present Value of an Ordinary Annuity
Interest and Time Value of Money Week 3
28
Present Value of an Ordinary Annuity
Time Year Amount Workings Present Value
Jan 1st 2009 0 $0 $0
Dec 31st 2009 1 $100 $89
Dec 31st 2010 2 $100 $80
Dec 31st 2011 3 $100 $71
Total $300 $240
Interest and Time Value of Money Week 3
29
Present Value of an Ordinary Annuity
$0
$20
$40
$60
$80
$100
$120
Amount
PresentValue
Amount $0 $100 $100 $100
Present Value $0 $89 $80 $71
Jan 1st 2009 Dec 31st 2009 Dec 31st 2010 Dec 31st 2011
Interest and Time Value of Money Week 3
30
Present Value of an Ordinary Annuity Using the Formula
rr
IPVAn
ORDINARY
1
11
where
• I = periodic investment
• r = interest rate per period
• n = number of periodsInterest and Time Value of Money
Week 3
31
At the beginning of each year an
investor deposits $10,000 into an
account which offers 10% p.a.
compound interest. What is the present
value of the investment if this is done
over 4 years?
Question 5
Interest and Time Value of Money Week 3
32
At the end of each year for 5 years an
investor deposits $2,000 into an
account which offers 2% p.a.
compound interest. What is the
present value of the investment?
Question 6
Interest and Time Value of Money Week 3
33
At the end of each quarter an investor
deposits $400 into an account which
offers 12% p.a. compound interest.
What is the present value of the
investment if this is done over 1
year?
Question 7
Interest and Time Value of Money Week 3
34
At the beginning of each month for 6
months an investor deposits $100 into
an account which offers 12% p.a.
compound interest. What is the
present value of the investment?
Question 8
Interest and Time Value of Money Week 3