Page 614 - Accounting Principles (A Business Perspective)

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Interest tables ease the task of computing the future worth to which any invested amount will grow at a given
rate for a stated period. An example is Table A.1 in the Appendix at the end of this text. To use the Appendix tables,
first determine the number of compounding periods involved. A compounding period may be any length of time,

such as a day, a month, a quarter, a half-year, or a year, but normally not more than a year. The number of
compounding periods is equal to the number of years in the life of the investment times the number of
compoundings per year. Five years compounded annually is five periods, five years compounded quarterly is 20
periods, and so on.
Second, determine the interest rate per compounding period. Interest rates are usually quoted in annual terms;
in fact, federal law requires statement of the interest rate in annual terms in some situations. Divide the annual rate
by the number of compounding periods per year to get the proper rate per period. Only with an annual

compounding period will the annual rate be the rate per period. All other cases involve a lower rate. For example, if
the annual rate is 12 per cent and interest is compounded monthly, the rate per period (one month) will be 1 per
cent.
To use the tables, find the number of periods involved in the Period column. Move across the table to the right,
stopping in the column headed by the Interest Rate per Period, which yields a number called a factor. The factor
shows the amount to which an investment of USD 1 will grow for the periods and the rate involved. To compute the
future worth of the investment, multiply the number of dollars in the given situation by this factor. For example,
suppose your parents tell you that they will invest USD 8,000 at 12 per cent for four years and give you the amount
to which this investment grows if you graduate from college in four years. How much will you receive at the end of

four years if the interest rate is 12 per cent compounded annually? How much will you receive if the interest rate is
12 per cent compounded quarterly?
To calculate these amounts, look at the end-of-text Appendix, Table A.1. In the intersection of the 4 period row
and the 12 per cent column, you find the factor 1.57352. Multiplying this factor by USD 8,000 yields USD 12,588.16,
the answer to the first question. To answer the second question, look at the intersection of the 16 period row and the
3 per cent column. The factor is 1.60471, and the value of your investment is USD 12,837.68. The more frequent
compounding would add USD 12,837.68 - USD 12,588.16 = USD 249.52 to the value of your investment. The

reason for this difference in amounts is that 12 per cent compounded quarterly is a higher rate than 12 per cent
compounded annually.
An annuity is a series of equal cash flows (often called rents) spaced equally in time. The semiannual interest
payments received on a bond investment are a common example of an annuity. Assume that USD 100 will be
received at the end of each of the next three semiannual periods. The interest rate is 6 per cent per semiannual
period. Using Table A.1 in the Appendix, we find the future value of each of the USD 100 receipts as follows:

Accounting Principles: A Business Perspective 615 A Global Text