Lecture 6Investments

Partial Payments

Ana Nora EvansOffice Hours:Mon 1:00-2:30Wed 3:30 -5:00 403 KerchofAnaNEvans@virginia.eduhttp://people.virginia.edu/~ans5k/

Math 1140 Financial Mathematics

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College Deadlines

Last day to add a class is Tuesday, Sep 6.Last day to drop a class is Wednesday, Sep 7.

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Previous lecturesHomework 3Lecture notes

Questions?

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Problem 1 2008 is a leap year! ordinary interestProblem 2 work with monthsProblem 3 typo in the printed page the net is due in 60 days example 1.4.4 on page

15

Problem 4 The note matures to

$40,000 means that the maturity value of the note is $40,000.

Problem 5 Not an add-on loan!Problem 6 Today’s lecture

Homework 3

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Simple debt instrumentsDiscounting a note

Equations of ValueFocal dateGolden Rule of Finance

Terms from last time

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Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 15% simple interest.

Amount 2 = maturity value of a 10% simple interest loan with term x days.

Correct/Incorrect question

A) Amount 1 < Amount 2B) Amount 2 < Amount 1C) Amount 1 ≤ Amount 2D) Amount 2 ≤ Amount 1E) None of the above (it

depends on the principal and the sale date)

Pledged quiz – No collaboration

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Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 15% simple interest.

Amount 2 = maturity value of a 10% simple interest loan with term x days

The correct answer is A. Amount 1 = 1.1P/(1 + 0.15(1 –

x/365))Amount 2 = P( 1 + 0.1x/365)

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Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 10% simple interest.

Amount 2 = maturity value of a 10% simple interest loan with term x days.

Participation question

A) Amount 1 < Amount 2B) Amount 2 < Amount 1C) Amount 1 ≤ Amount 2D) Amount 2 ≤ Amount 1E) None of the above( It

depends on the principal and the sale date.)

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Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 10% simple interest.

Amount 2 = a 10% simple interest loan with term x days.

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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.

The net present value (NPV) is the income minus expenses, all moved to the present.

The internal rate of return (IRR) is the rate at which the returns and investments make the NPV zero.

Investments

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An easier way to think about NPV:

use plus sign for incomeuse minus sign for expensesmove everything to the presentadd them all

IRR is difficult to calculate.

It is difficult to predict accurately the returns.

The returns may be irregular.

NPV and IRR

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Bob buys an old house for $50,000. He spends $10,000 to fix it and he sells it in six months for $75,000.

What is NPV (net present value) at 15% simple interest?

What is IRR (internal rate of return)?

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Math can get more complicated

If the investment brings returns at two different dates you will need to solve a quadratic equation.

If the investment brings returns at three different dates you will need to solve a cubic equation.

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y2 = d ax2 + bx + c = 0

Quadratic equation formula

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Email Questions

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For a simple interest loan, the borrower is not required to make any payments until the due date.

The borrower and the lender may agree how any partial payments will reduce the interest charges.

Merchant’s RuleSet the focal date to be the due

date.Use an equation of value to

determine the balance on the loan.

The maturity value is negative.The partial payments (moved to

the focal date) are positive.

Partial Payments

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Merchant’s Rule

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At the date of a partial payment, the balance is calculated and it becomes the new principal of a simple interest loan with start date the date of the partial payment and due date the original due date.At the due date, the leftover balance is due.

The principal is negative.The payments are positive.To calculate the balance: add the principal add the interest add payment

United States Rule

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Next time

Discount Interest

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Due Wednesday:Read Sections 2.1 and

2.2 Third homeworkOffice Hours : Monday 1:00-2:30 pm Tuesday 3:30-5:00 pm

First Exam (max 15 points): 26 September 2011 at 7pm Location to be announced

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