Math 1140 Financial Mathematics Lecture 5 Equations of Value Ana Nora Evans 403 Kerchof...

Math 1140 Financial Mathematics

Lecture 5Equations of

Value

Ana Nora Evans403 [email protected]://people.virginia.edu/~ans5k/

2Math 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”


McDonalds


Best Buy


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!


Homework 3

For exercises 2, 4, 5 calculate the term using months!

If you find my typed version confusing, use the textbook!


Questions?


Terms from last time

Add-on loan

Discount for prompt payment


Maturity(Future) Value


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.


Present and Future Value

Your grandma sends you a $500 check for your birthday.

What is the value of the $500 on your birthday?

What is the value of the $500 four years from now?


Past value

What was the value of the $500 four years ago?A) 0B) $500C) More than $500D) Less than $500

This is a participation question.


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?


Conclusion

Money has value at all times – now, in the past and in the future.


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.


Why is the US Capital where it is?


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


Simple Debt Instruments

A debt instrument is a legal document showing evidence of a debt.


Promissory Note

A legal document specifying the terms of a loan: the principal the terms of repayments the interest rate the date the maturity dateDifferent from IOU and loan contract.


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.


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.


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


Unknown

P2 – the price Unsuspecting Investor pays to Shady Bank


Solution

Step 1 - Calculate the maturity value

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


Solution

Step 2 – Discount the maturity valueThis means to calculate the present value at

time d2

We use the formula for present value:

22

2

1 ti

SP


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.


Solution


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.


The Golden Rule of Finance

Monies cannot be added or reconciled unless they are valued at the same point in time.


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.


Example

You win the darts contest at your favorite watering hole and have a choice of how to receive your prize.

Option 1: $750 nowOption 2: $500 in three years and $550 in seven

yearsIf money can be invested at 10% simple interest

which option would you choose?


Solution


Charge

Due Monday:Read section 1.9

Due Wednesday :Third homework

Math 1140 Financial Mathematics Lecture 5 Equations of Value Ana Nora Evans 403 Kerchof...

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