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Math 1140 Financial Mathematics
Lecture 5
Equations of
Value
Ana Nora Evans403 [email protected]://people.virginia.edu/~ans5k/
Math 1140 - Financial Mathematics
Homework comments
Some of you really tried to understand the
details of you credit card agreement. Most of
you did not.
I got some great answers in the last problem.
The return on investment is not realistic!
“… which method is more advantageous
totally depends on the risk and stock quality”
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McDonalds
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Best Buy
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Projects
Based on the second homework
quality I am anticipating very
interesting projects.
Start thinking about what you would
like to do and with whom!
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Homework 3
For exercises 2, 4, 5 calculate the term using
months!
If you find my typed version confusing, use the
textbook!
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Questions?
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Terms from last time
Add-on loan
Discount for prompt payment
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Maturity(Future) Value
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Present Value
We know the term, interest rate and the
maturity value (future value).
We want to know how much we need to invest
today.
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Present and Future Value
Your grandma sends you a $500 check for your
birthday.
What is the value of the $500 on your birthday?
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What is the value of the $500 four years from
now?
Math 1140 - Financial Mathematics
Past value
What was the value of the $500 four years ago?
A) 0
B) $500
C) More than $500
D) Less than $500
This is a participation question.
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Let’s see
What was the value of the $500 four years ago?
is the same as
How much money would you have had to invest
four years ago?
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Conclusion
Money has value at all times – now, in
the past and in the future.
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Math 1140 - Financial Mathematics
Fourteenth Amendment
Section 4. The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned. But neither the United States nor any State shall assume or pay any debt or obligation incurred in aid of insurrection or rebellion against the United States, or any claim for the loss or emancipation of any slave; but all such debts, obligations and claims shall be held illegal and void.
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Why is the US Capital where it is?
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This broke out on every question with the most alarming heat,
the bitterest animosities seemed to be engendered, and tho’
they met every day, little or nothing could be done from
mutual distrust and antipathy.... It ended in Mr. Madison’s
acquiescence in a proposition that the question should be
again brought before the House by way of amendment from
the Senate, that tho’ he would not vote for it, nor entirely
withdraw his opposition, yet he should not be strenuous, but
leave it to its fate. It was observed, I forget by which of them,
that as the pill would be a bitter one to the Southern states,
something should be done to soothe them; that the removal of
the seat of government to the Potomac was a just measure,
and would probably be a popular one with them, and would be
a proper one to follow the assumption.
Thomas Jefferson, Memorandum on the Compromise of 1790
Math 1140 - Financial Mathematics
Simple Debt Instruments
A debt instrument is a legal document
showing evidence of a debt.
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Promissory Note
A legal document specifying the terms of a loan:
the principal
the terms of repayments
the interest rate
the date
the maturity date
Different from IOU and loan contract.
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Discounting the note
A debt instrument can be sold for less than
the maturity value. This is called
discounting the note.
The terms of the loan do not change for
the borrower.
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Possible Scenario
A subprime borrower takes out a simple interest
rate loan from Shady Bank with a certain
maturity date and interest rate.
Shady Bank decides the risk is too high and sells
the loan to the Unsuspecting Investor who
wants a higher interest rate.
The problem is to calculate the sell price.
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Given data
P – the principal
i1 – the original interest rate of the loan
d1 – the date of the loan
d3 – the maturity date
i2 – the interest rate desired by the buyer of
the loan
d2 – the sale date
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Unknown
P2 – the price Unsuspecting Investor pays to
Shady Bank
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Solution
Step 1 - Calculate the maturity value
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We use the formula for future value:
S = P( 1 + i1t1)
t1 is the (exact) time from d1 to d3
S is the value of the principal at time d3
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Solution
Step 2 – Discount the maturity value
This means to calculate the present value at
time d2
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We use the formula for present value:
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2
1 ti
SP
+
=
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Example
Bob holds a promissory note signed by Alice on
23 August 2011. The note is for $1,000 at 12%
simple interest with a maturity date of 23
March 2012. On 23 December 2011, Bob sells
the note to Katie who wants 15% simple
interest.
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Solution
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Equations of Value
A focal date is a chosen date to evaluate the
money.
An equation of value is a mathematical
expression involving several pieces of money
at a focal date.
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The Golden Rule of Finance
Monies cannot be added or reconciled unless
they are valued at the same point in time.
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Investments
Goal: predict if an investment will give a good
rate of return.
The rate of return of an investment is the ratio
of money gain or lost relative to the money
invested.
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Math 1140 - Financial Mathematics
Example
You win the darts contest at your favorite
watering hole and have a choice of how to
receive your prize.
Option 1: $750 now
Option 2: $500 in three years and $550 in seven
years
If money can be invested at 10% simple interest
which option would you choose?
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Solution
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Charge
Due Monday:
Read section 1.9
Due Wednesday :
Third homework
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