Accounting: The Language of Business - Vol. 2 (Intermediate: Part 92)

The more science learns, the clearer it is that although we are here, we shouldn't be. Once we begin considering the details of it all, the towering odds against our existence begin to become a bit unsettling. When we come to see the superlatively extreme precariousness of our existence, and begin to understand how by any accounting, we ought not to exist, what are we to think or feel? Our existence seems to be not merely a virtually impossible miracle but the most outrageous miracle conceivable, one that makes previously amazing miracles seem like almost nothing.

Eric Metaxas

 Accounting and the Time Value of Money (Part E)

by

Charles Lamson

Factor Table Solution. We can also solve future value problems using factor tables. A factor is a number derived from a combination of an interest rate and compounding period that can be multiplied by an amount to obtain the value needed. Instead of using the formula, the factor is a shortcut to compute the needed value. To illustrate, let's develop the future value of 1 dollar ($1) compounding factors using the future value formula from Equation 7.2. If N = 40, I / Y = 2%, and PV = $1 as in Example 7.5, then the future value is: 

With a deposit of $1, the FV after 40 periods when the interest rate is 2% is equal to $2.21 (rounded), as obtained above.

Table 7A.1 below presents the complete set of compound interest factors for future value of $1 factors for solving future value problems. Rows of the table represent the number of compounding periods. Columns have the interest rate per compounding period. The amount presented in the cell for each row and column is computed from Equation 7.2: It is the factor for a future value of $1 for the given interest rate and number of periods. We use the 2% column and then search down to the 40-period row to locate the factor 2.20804 that was derived above using the formula.

TABLE 7A.1 Future Value of $1

Click to enlarge.

The factors in table 7A.1 illustrate that the future value is directly related to N and I / Y. We can now use the factors from Table 7A.1 in Equation 7.3 to solve single sum future value problems:

 

To solve for the future value, find the factor that is in the row for the number of corresponding periods and the column for the interest rate per compounding period. Multiply this factor times the present value to obtain the future value. Example 7.6 demonstrates the table approach.

Spreadsheet Solution. A spreadsheet application such as Microsoft Excel is another way to solve future value problems. The future value function in a spreadsheet cell follows:

= FV ( I/Y,N,PMT,PV,type)

For the future value of a single sum, we put zero in the third position because there are no periodic payments. Because the type defaults to 0, we do not need to include the last variable because we do not have an annuity problem. In the spreadsheet examples, we use the convention of designating borrowing or receiving payments as cash inflows and lending or investing money as cash outflows. In the time value of money spreadsheet computations, cash inflows are positive values and cash outflows are negative values. Example 7.7 illustrates the spreadsheet approach.

*GORDON, RAEDY, SANNELLA, 2019, INTERMEDIATE ACCOUNTING, 2ND ED., PP. 321-323*

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