Maths of Finance_w ans

Maths of Finance_w ans - 10 Chapter 2 - Mathematics of...

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10 Chapter 2 -- Mathematics of Finance 1 Interest Rates and Economic Theory Why, when you deposit money in a savings account, does the bank pay you interest? Why, when you borrow money to purchase a home, car or holiday, does the lender charge you interest? Economic theory explains the existence of a positive rate of interest in the following ways: (a) Money can be thought of as an asset used to engender a return, as it buys assets which derive returns. For a money holder to lend and forego the opportunity to buy assets, a rent is charged, equivalent to the returns on the productive assets which the money could have purchased. (b) A consumer needs an economic incentive to postpone consumption from the present to some time in the future. The lender of money is doing just this by reducing their possible present consumption for future consumption. 2 The Rate Of Interest In The Real World Many different rates of interest coexist and fluctuate over time. The experience of the last few years has seen interest rates vary markedly. These fluctuations can in part be attributed to macroeconomic factors. However, this is also explained by the three main components of the "nominal" rate of interest. (a) The real rate of interest "r". This is the financial reward for lending money or postponing consumption as discussed in the previous section. (b) A risk premium "d". This is compensation for the uncertainty of whether the principal and/or interest will be repaid when due. (c) Expected changes in the price level "p". When prices increase, the principal and interest repaid by the borrower at some future time have decreased in purchasing power. The lender will seek an equivalent compensation for this loss. In periods of high sustained price growth it is likely that lenders' expect inflation to continue. These expectations are incorporated into prevailing interest rates. We could thus write the nominal rate, n r , as an additive function of its three components: n r = r + d + p The above factors can be used to explain, in part, the existence of different interest rates in the economy and their fluctuations over time, such as why commercial rates differ from mortgage rates. We will focus on the real rate of interest, assuming the other factors are negligible. For our purposes, n r = r, and will be expressed on a yearly (per annum) basis, as this is the way interest rates are conventionally quoted.
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11 3 Simple Interest Suppose you have an amount $P to invest for one year at interest rate "r". At the end of the year the interest reward is "P.r". The amount $P if invested for n years using simple interest will collect "P.r.n". Simple interest assumes that interest is only calculated on the original principal and no interim rewards generate additional interest.
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This note was uploaded on 04/14/2010 for the course ECMT 1010 taught by Professor Vadimtimovsky during the Three '10 term at University of Sydney.

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Maths of Finance_w ans - 10 Chapter 2 - Mathematics of...

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