Fundamentals of Financial Instruments. Sunil K. Parameswaran
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Название: Fundamentals of Financial Instruments

Автор: Sunil K. Parameswaran

Издательство: John Wiley & Sons Limited

Жанр: Ценные бумаги, инвестиции

Серия:

isbn: 9781119816638

isbn:

СКАЧАТЬ rel="nofollow" href="#fb3_img_img_e5b34fa8-6875-5402-856d-1867bbadb545.png" alt="upper P left-parenthesis 1 plus r right-parenthesis Superscript upper N Baseline equals 25 comma 000 times left-parenthesis 1.08 right-parenthesis Superscript 4.75 Baseline equals dollar-sign 36 comma 033.20"/>

      In the earlier case, when we assumed simple interest, we got a value of $34,500.

      As can be seen from the examples, compounding yields substantially greater benefits than simple interest. And since the rate of interest is taken to the power of N, the larger the value of N, the greater will be the impact of compounding. In other words, the earlier one starts investing, the greater will be the returns.

      EXAMPLE 2.6

      Jesus was born approximately 2,000 years ago. Assume that an investment of $1 was made in that year in a bank that has been paying 1% interest per annum since then, compounded annually. What will be the accumulated balance in the year 2000?

1 times left-parenthesis 1.01 right-parenthesis Superscript 2000 Baseline equals dollar-sign 439 comma 286 comma 205

       If N = 1, that is, an investment is made for one period, both the simple and compound interest techniques will give the same accumulated value.In the case of Katherine, the value of her initial investment of $25,000 at the end of the first year was $27,000, irrespective of whether simple or compound interest was used.

       If N < 1, that is, the investment is made for less than a period, the accumulated value using simple interest will be higher. That isFor instance, assume that Katherine deposits $25,000 for nine months at a rate of 8% per annum compounded annually. If interest is calculated on a simple interest basis, she will receiveOn the other hand, compound interest would yield

       If N > 1, that is, the investment is made for more than a period, the accumulated value using compound interest will always be greater. That isAs can be seen, if Katherine were to invest for four years, simple interest will yield $33,000 at the end, whereas compound interest will yield $34,012.2240.

      Note 1: The word period used here to demonstrate the properties of simple and compound interest should be interpreted as the interest conversion period. In our illustrations, the interest was compounded once per year, so there was no difference between the measurement period and the conversion period; however, take the case where interest is paid at 8% per annum compounded quarterly. If so, the above properties may be stated as follows.

       If the investment is made for one quarter, both simple and compound interest will yield the same terminal value.

       If the investment is made for less than a quarter, the simple interest technique will yield a greater terminal value.

       If the investment is made for more than a quarter, the compound interest technique will yield a greater terminal value.

      Simple interest is usually used for short-term or current account transactions, that is, for investments for a period of one year or less. Consequently, simple interest is the norm for money market calculations. The term money market refers to the market for debt securities with a time to maturity at the time of issue of one year or less. In the case of capital market securities, however – that is, medium- to long-term debt securities and equities – we use the compound interest principle. Simple interest is also at times used as an approximation for compound interest over fractional periods.

      EXAMPLE 2.7

      Take the case of Alex Gunning, who deposited $25,000 with International Bank for four years and nine months. Assume that the bank pays compound interest at the rate of 8% per annum for the first four years and simple interest for the last nine months.

      The balance at the end of four years will be

25 comma 000 times left-parenthesis 1.08 right-parenthesis Superscript 4 Baseline equals 34 comma 012.22

      The terminal balance will be

34 comma 012.22 times left-parenthesis 1 plus 0.08 times 0.75 right-parenthesis equals dollar-sign 36 comma 052.96

      In the earlier case when interest was compounded for four years and nine months, the accumulated value was $36,033.20. Thus, simple interest for the fractional period yields an additional benefit of $19.76. The reason why we get a higher value in the second case is that for a fractional period simple interest will give a greater return than compound interest.

      Effective Versus Nominal Rates of Interest

      EXAMPLE 2.8

      ING Bank is quoting a rate of 8% per annum compounded annually on deposits placed with it, whereas HSBC is quoting 7.80% per annum compounded monthly on funds deposited with it. A naïve investor may be tempted to conclude that ING is offering better returns, as its quoted rate is higher. It is important to note, however, that the compounding frequencies are different. While ING is compounding on an annual basis, HSBC is compounding every month.

      From our earlier discussion, we know that since ING is compounding only once a year, the effective rate offered by it is the same as the rate quoted by it, which is 8% per annum. However, since HSBC is compounding on a monthly basis, its effective rate will obviously be greater than the rate quoted by it. The issue is, is the effective rate greater than 8% per annum?

      7.80% per annum corresponds to 7.80 slash 12 equals 0.65 percent-sign per month. Consequently, if an investor were to deposit $1 with HSBC for a period of one year, or 12 months, the terminal value would be

1 times left-parenthesis 1.0065 right-parenthesis Superscript 12 Baseline equals 1.08085

      Consequently, a rate of 7.80% per annum compounded monthly is equivalent to receiving a rate of 8.085% with annual compounding. The phrase effective annual rate connotes that effectively the investor who deposits with HSBC receives a rate of 8.085% compounded on an annual basis.

      Thus, when the frequencies of compounding are different, comparisons between alternative investments ought to be based on the effective rates of interest and not on the nominal rates. In our case, an investor who is contemplating a deposit of say $10,000 for a year would choose to invest with HSBC despite the fact that its quoted or nominal rate is lower.

      Note 2: It must be remembered that the distinction between nominal and effective rates is of relevance only when compound interest is being paid. The concept is of no consequence if simple interest is being paid.