ENG 2001 Lecture Notes - Lecture 2: Guaranteed Investment Certificate, Real Interest Rate, Cash Flow
26 Jun 2018
School
Department
Course
Professor
1
ENG2001
Time Value of Money
Professor Jinjun Shan
ESSE
Time value of money
• One of the main reasons for the complexity in
engineering economics is that the value of money is
not constant
• For example, if you borrow money on your credit
card, you have to pay interest
• Conversely, if you invest the same money now, you
can afford more at a future date
• In engineering projects, the sums of money can be
large, so it makes a big difference how something is
paid for
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2
• The essence of the problem is therefore… “how do we compare
options when we consider the time value of money?”
• Why are there interest rates?
– because the lender could have done something of value
with the money that you now have
– so it costs them to lend you the money
– interest is therefore the compensation that the borrower
pays to the lender for the loss of use of their money
• Hence money has both a present worth and a future worth
– or a dollar today is worth more than a dollar at a future time
Time value of money
Example
• Samuel bought a one-year guaranteed investment certificate
(GIC) for $5,000 from a bank on 15 May 2002. The bank
was paying 10% on one-year GICs at that time. On 15 May
2003, he will cash the GIC for $5,500.
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3
• Interest (I) is the difference between the present worth
(P) and the future worth (F)
– the interest rate (i) expresses how the total
interest is accumulated as a function of time
P
I
future worth, F
interest, I
P
present worth, P
(also called principal)
1 period
interest rate, i
F=P+I
I=Pi
F=P+Pi =P1+i
( )
Example
• In the example, Samuel traded $1 on 15 May 2002 for the right to collect
$1.1 on 15 May 2003
– $5500/$5000 = 1.1
– hence, P = $1, F = $1.1, I = $0.1
– for the 1-year period, the interest rate, i = 0.1 = 10%
– the dimensions of interest rate are:
(dollars/dollars)/(time period)
Example
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Document Summary
Because the lender could have done something of value with the money that you now have. Or a dollar today is worth more than a dollar at a future time. Example: samuel bought a one-year guaranteed investment certificate (gic) for ,000 from a bank on 15 may 2002. The bank was paying 10% on one-year gics at that time. 2003, he will cash the gic for ,500. Example: interest (i) is the difference between the present worth (p) and the future worth (f) The interest rate (i) expresses how the total interest is accumulated as a function of time present worth, p (also called principal) F = p + pi = p 1+ i. In the example, samuel traded on 15 may 2002 for the right to collect. Hence, p = , f = . 1, i = sh. 1 for the 1-year period, the interest rate, i = 0. 1 = 10% the dimensions of interest rate are: (dollars/dollars)/(time period)
