Accounting: The Language of Business - Vol. 2 (Intermediate: Part 95)

Now, that’s my boy you’re talking about, and I don’t want to get crossed up with you, Sasha. But you keep that tone and attitude about him, and we will.” – Sundown “Sorry. I forget you and Ash are weird enough to actually like him. No accounting for taste.” – Sasha

Sherrilyn Kenyon

Accounting and the Time Value of Money (Part H)

by

Charles Lamson

Other Single-Sum Problems

As we have discussed in Part 91, there are four variables in the single-sum problems. Typically, problems either solve for the present value or future value. However, at times the present and future values are known factors and solutions require solving for either the interest rate for the compounding period or the number of compounding periods.

Solving for the Interest Rate. We illustrate solving for the interest rate when we have the other three variables—FV, PV, N.

To solve for the interest rate with a formula, we rearranged the variables in equation 7.2 (from Part 92 and reintroduced below) to arrive at equation 7.6:

 

EXAMPLE 7.11 Solving for the Interest Rate in a Single-Sum Problem

To use the factor tables, start on the inside cells of the table. Referring to Table 7A.1 (from Part 92 and reintroduced below), we know from Equation 7.3 that the FV equals the PV times the table 7A.1 factor.

TABLE 7A.1 Future Value of $1

Click to enlarge. 

Thus, solving for the interest rate involves:

1. Computing the left-hand side of the equation by dividing future value by present value.

2. Searching for the interest rate in the row corresponding to the number of compounding periods (finding a factor in the table will depend on interest rates and the number of periods presented. If a factor is not found in a table, use another approach such as the formula or spreadsheet.

EXAMPLE 7.12 Solving for the Interest Rate in a Single-Sum Problem

We solve for the interest rate variable, I/Y, using the rate function in a spreadsheet cell as follows:

= RATE(N,PMT,PV,type)

All variables are previously defined. To solve the problem in Example 7.12, enter the following amounts in each cell.

The spreadsheet provides the solution, 4.00%.

We can solve interest rate problems using a financial calculator. To solve the problem in example of 7.12, enter the following keystrokes.

 The calculator shows the interest rate is 4%. 

*GORDON, RAEDY, SANNELLA, 2019, INTERMEDIATE ACCOUNTING, 2ND ED., PP. 327-329*

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