Accounting and the Time Value of Money
(L.O. 1) Chapter 6 discusses the essentials of compound interest, annuities and present value. These techniques are being used in many areas of financial reporting where the relative values of cash inflows and outflows are measured and analyzed. The material presented in Chapter 6 will provide a sufficient background for application of these techniques to topics presented in subsequent chapters.
Compound interest, annuity, and present value techniques can be applied to many of the items found in financial statements. In accounting, these techniques can be used to measure the relative values of cash inflows and outflows, evaluate alternative investment opportunities, and determine periodic payments necessary to meet future obligations. Some of the accounting items to which these techniques may be applied are: (a) notes receivable and payable, (b) leases, (c) pensions, (d) long-term assets, (e) sinking funds, (f) business combinations, (g) disclosures, and (h) installment contracts.
Nature of Interest
(L.O. 2) Interest is the payment for the use of money. It is normally stated as a per-centage of the amount borrowed (principal), calculated on a yearly basis. For example, an entity may borrow $5,000 from a bank at 7% interest. The yearly interest on this loan is $350. If the loan is repaid in six months, the interest due would be 1/2 of $350, or $175. This type of interest computation is known as simple interest because the interest is computed on the amount of the principal only. The formula for simple interest can be expressed as p x i x n where p is the principal, i is the rate of interest for one period, and n is the number of periods.
(L.O. 2) Compound interest is the process of computing interest on the principal plus any interest previously earned. Referring to the example in (3) above, if the loan was for two years with interest compounded annually, the second year’s interest would be $374.50 (principal plus first year’s interest multiplied by 7%). Compound interest is most common in business situations where large amounts of capital are financed over long periods of time. Simple interest is applied mainly to short-term investments and debts due in one year or less. How often interest is compounded can make a substantial difference in the level of return achieved.
In discussing compound interest, the term period is used in place of years because interest may be compounded daily, weekly, monthly, and so on. Thus, to convert the annual interest rate to the compounding period interest rate, divide the annual interest rate by the number of compounding periods in a year. Also, the number of periods over which interest will be compounded is calculated by multiplying the number of years involved by the number of compounding periods in a year.
Compound Interest Tables
(L.O. 3) Compound interest tables have been developed to aid in the computation of present values and annuities. Careful analysis of the problem as to which compound interest tables will be applied is necessary to determine the appropriate procedures to follow.
The following is a summary of the contents of the five types of compound interest tables:
“Future value of 1” table. Contains the amounts to which 1 will accumulate if deposited now at a specified rate and left for a specified number of periods. (Table 1)
“Present value of 1” table. Contains the amount that must be deposited now at a specified rate of interest to equal 1 at the end of a specified number of periods. (Table 2)
“Future value of an ordinary annuity of 1” table. Contains the amount to which periodic rents of 1 will accumulate if the rents are invested at the end of each period at a specified rate of interest for a specified number of periods. (This table may also be used as a basis for converting...
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