# AN INTRODUCTION TO THE MATHEMATICS OF FINANCE MCCUTCHEON PDF

This book is a revision of the original An Introduction to the Mathematics of. Finance by J.J. McCutcheon and W.F. Scott. The subject of financial. By J. J. McCutcheon and W. F. Scott. | An Introduction to the Mathematics of Finance. By McCutcheon J. J. and Scott W. F.. - Volume Issue 3 - Simon Carne. Introduction to the Mathematics of Finance 2ed [] - Ebook download as PDF File .pdf), Text File .txt) or read book online. book is necessarily mathematical, but I hope not too mathematical. Finance by J.J. McCutcheon and W.F. Scott.

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for the subject CT1 (Financial Mathematics) of the Actuarial Profession. The .. in financial mathematics the profitability of an investment for a short period of time of [2] J.J. McCutcheon, W.F. Scott. An Introduction to the Mathematics of Fi-. mathematics of finance. We calculate an accumulated amount of some special im - mediate annuities by solving the special type of non-homogenous linear. An Introduction to the Mathematics of Finance: A Deterministic Approach P.D.F. This revision of the McCutcheon-Scott classic follows the core.

Continuously Payable Annuities -- 3. Varying Annuities -- 3. Uncertain Payments -- Summary -- Exercises -- 4. Interest Payable pthly -- 4. Annuities Payable pthly: Present Values and Accumulations -- 4. Definition of an p for Non-integer Values of n -- Summary -- Exercises -- 5. The General Loan Schedule -- 5. The Loan Schedule for a Level Annuity -- 5.

The Loan Schedule for a pthly Annuity -- 5. Consumer Credit Legislation -- Summary -- Exercises -- 6. Net Cash Flows -- 6. Net Present Values and Yields -- 6. The Comparison of Two Investment Projects -- 6. Different Interest Rates for Lending and Borrowing -- 6.

Payback Periods -- 6. The Effects of Inflation -- 6. Fixed-Interest Securities -- 7. Related Assets -- 7. Prices and Yields -- 7. Perpetuities -- 7. Makeham's Formula -- 7. The Effect of the Term to Redemption on the Yield -- 7. Optional Redemption Dates -- 7. Optional Redemption Dates -- 8.

## Introduction to the Mathematics of Finance 2ed []

Spot and Forward Rates -- 9. Theories of the Term Structure of Interest Rates -- 9. The Discounted Mean Term of a Project -- 9. Volatility -- 9. The Volatility of Particular Fixed-interest Securities -- 9. The Matching of Assets and Liabilities -- 9. Redington's Theory of Immunization -- 9. Full Immunization -- Summary -- Exercises -- Net present value of a sequence of cashflows.

Equation of value. Internal rate of return. Investment project appraisal. Examples of cashflow patterns and their present values. Elementary compound interest problems.

Samuel A. Broverman, Mathematics of Investment and Credit, 4th ed. Core reading for the examinations. Stephen G. Kellison, The Theory of Interest, 3rd ed.

## Related titles

Brown, Mathematics of Finance, 2nd ed. The book 2 describes the first exam that you need to pass to become an accredited actuary in the UK. It is written in a concise and perhaps dry style.

These lecture notes are largely based on Book 4. Book 5 contains many exercises, but does not go quite as deep. Book 3 is written from a U. Book 1 is written by a professor from a U. All these books are useful for consolidating the course material.

**Other books:**

*EXPLORING THE WORLD OF LUCID DREAMING EBOOK*

They allow you to gain background knowledge and to try your hand at further exercises. However, the lecture notes cover the entire syllabus of the module. Tuesdays to be determined or whenever you find the lecturer and he has time. There will be five sets of course work. Put your work in your tutor s pigeon hole on Level 8 of School of Mathematics. One mark out of ten will be deducted for every day.

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Collaboration is allowed even encouraged , copying not. See the student handbook for details.

The exam will take place in the period 14 May 30 May; exact date and location to be announced. For instance, suppose that you put some money on a bank account for a year. Then, the bank can do whatever it wants with that money for a year. To reward you for that, it pays you some interest. The asset being lent out is called the capital. Usually, both the capital and the interest is expressed in money. However, that is not necessary. In this course, the capital is always expressed in money, and in that case it is also called the principal.

There are various methods for computing the interest. As the name implies, simple interest is easy to understand, and that is the main reason why we talk about it here. The idea behind simple interest is that the amount of interest is the product of three quantities: the rate of interest, the principal, and the period of time. However, as we will see at the end of this section, simple interest suffers from a major problem. For this reason, its use in practice is limited.

Definition Simple interest. The interest earned on a capital C lent over a period n at a rate i is nic. And if you leave it in the account for only half ar year? In this MATH 1 8 example, the period is measured in years, and the interest rate is quoted per annum per annum is Latin for per year. These are the units that are used most often.

In Section 1. How much do you have in the end? Now compare Examples and The first example shows that if you invest for two years, the capital grows to But the second example shows that you can get by switching accounts after a year. Even better is to open a new account every month. This inconsistency means that simple interest is not that often used in practice. Instead, savings accounts in banks pay compound interest, which will be introduced in the next section.

Nevertheless, simple interest is sometimes used, especially in short-term investments. Exercises 1. The idea behind compound interest is that in the second year, you should get interest on the interest you earned in the first year.

In other words, the interest you earn in the first year is combined with the principal, and in the second year you earn interest on the combined sum. The capital is multiplied by 1. Definition Compound interest. This is 97p less than the 45 pounds interest you get if the account would pay simple interest at the same rate see Example 1.

Example Suppose that a capital of dollars earns dollars of interest in 6 years. What was the interest rate if compound interest is used? What if simple interest is used? Note that the computation is the same, regardless of the currency used. What if the account pays simple interest? Then take logarithms: log 1. Note that it does not matter how much you have at the start: it takes as long for one pound to grow to two pounds as for a million pounds to grow to two million.

The computation is simpler for simple interest. Thus, we get n log 2 i. This is known as the rule of 72 : To calculate how many years it takes you to double your money, you divide 72 by the interest rate expressed as a percentage.

The rule of 72 can already be found in a Italian book from Summa de Arithmetica by Luca Pacioli. The use of the number 72 instead of Remember that with simple interest, you could increase the interest you earn by withdrawing your money from the account halfway. Compound interest has the desirable property that this does not make a difference. Suppose that you put your money m years in one account and then n years in another account, and that both account pay compount interest at a rate i.

This is the reason why compound interest is used so much in practice. Unless noted otherwise, interest will always refer to compound interest. Find the accumulation of after seven years in this account.

The right figure plots the amount of capital after 5 years for various interest rates. The dashed line is for simple interest and the solid curve for compound interest. We see that compound interest pays out more in the long term. A careful comparison shows that for periods less than a year simple interest pays out more, while compound interest pays out more if the period is longer than a year. This agrees with what we found before.

The difference between compound and simple interest get bigger as the period gets longer. These will not be proven here. The right plot in Figure 1. However, the plot also shows that the difference is smaller if the interest rate is small. This can be explained with the theory of Taylor series.

Thus, you can use the formula for simple interest as an approximation for compound interest; this approximation is especially good if the rate of interest is small. Especially in the past, people often used simple interest instead of compound interest, notwithstanding the inconsistency of simple interest, to simplify the computations.

We have seen how to calculate the interest rate Example 1. The one remaining possibility is covered in the next example.

## Compound Interest and Discount

We call the present value and the future value. When you move a payment forward in time, it accumulates; when you move it backward, it is discounted see Figure 1.

This shows that money has a time value: the value of money depends on the time now is worth more than in five years time. In financial mathematics, all payments must have a date attached to them. More generally, suppose the interest rate is i. How much do you need to 1 invest to get a capital C after one time unit? It is the factor with which you have to multiply a payment to shift it backward by one year see Figure 1.

In our example, the rate of discount is or 4. What is the present value of a payment of e70 in a year s time? Usually, interest is paid in arrears.

If you borrow money for a year, then at the end of the year you have to pay the money back plus interest. However, there are also some situations in which the interest is paid in advance.

The rate of discount is useful in these situations, as the following example shows. If you borrow e for a year and you have to pay interest at the start of the year, how much do you have to pay? MATH 7 14 Answer. However, you have to pay the interest one year earlier. As we saw in Example 1. There is another way to arrive at the answer.

At the start of the year, you get e from the lender but you have to pay interest immediately, so in effect you get less from the lender. At the end of the year, you pay e back.

The amount you should get at the start of the year should be equivalent to the e you pay at the end of the year. We found before, in equation 1.

## An Introduction to the Mathematics of Finance

We summarize this discussion with a formal definition of the three quantities d, i and v. Definition The rate of interest i is the interest paid at the end of a time unit divided by the capital at the beginning of the time unit.

The rate of discount d is the interest paid at the beginning of a time unit divided by the capital at the end of the time unit. The discount factor v is the amount of money one needs to invest to get one unit of capital after one time unit.

This definition concerns periods of one year assuming that time is measured in years. In Example 1. The same method can be used to find the present value of a payment of C due in n years if compound interest is used at a rate i. The question is: which amount x accumulates to C in n years? There is another method, called simple discounting analogous to simple interest or commercial discounting. This is defined as follows. The present value of a payment of C due in n years, at a rate of simple discount of d, is 1 nd c.

The present value of a payment of C due in n years, at a rate of simple interest of i, is the amount x that accumulates to C over n years. What is the corresponding rate of compound discount? And the rate of compound interest? And the rate of simple interest? One important application for simple discount is U. Treasury Bills. However, it is used even less in practice than simple interest.

In return for a loan of a borrower agrees to repay after seven months. Assuming that the lender agrees to the request and that the calculation is made on the original interest basis, find the amount of the second payment under the revised transaction. The loan is settled by a payment of after three months.

Compute the amount borrowed and the effective annual rate of discount.

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Answer the same question. MATH 9 16 1. Up to now, we assumed that interest is paid once a year. In practice interest is often paid more frequently, for instance quarterly four times a year.MATH 7 14 Answer. If this does. The loans are typically of short duration and to high-risk consumers. The equation of value or yield equation as stated in Eq.

It is desirable to consider this schedule in greater detail Close X. Introduction to the Mathematics of Finance. Treasury Bills.

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