Accounting: The Language of Business - Vol. 2 (Intermediate: Part 107)

“Talent is cheaper than table salt. What separates the talented individual from the successful one is a lot of hard work.”
— Stephen King

 Accounting and the Time Value of Money (Part Q)

by

Charles Lamson 

Other Annuity Problems 

In the annuity problems from the preceding parts of this analysis, we knew the interest rate, the payments, and the number of compounding periods and solved for either the present value or future value. However, there are times when you will be asked to solve for the interest rate, payments, or number of periods. We discuss these scenarios for ordinary annuities (series of equal payments made at the end of consecutive periods over a fixed length of time) in the next several parts. We discuss only ordinary annuities in these parts, but it is straightforward to extrapolate these procedures to the annuity due (annuity whose payment is due immediately at the beginning of each period) case.

Solving for the Interest Rate. To solve for the interest rate in an ordinary annuity problem, we could use Equation 7.13 from Part 102 and solve for I/Y,  but that is complex. Therefore, we present the other solution approaches.

Using the factor tables, start on the inside of the table. Referring to the present value of an ordinary annuity factors in Table 7A.5, we know from Equation 7.14 from Part 103

Thus, we compute the left hand side of the equation and search 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 7.27 Solving for the Interest Rate in an Ordinary Annuity Problem

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

= RATE(N,PMT,PV,FV,type)

All variables are previously defined. To solve the problem in Example 7.27, enter the following amounts in each cell. 

The spreadsheet provides the solution, 5.00%.

We can also solve for the interest rate in an ordinary annuity problem using a financial calculator. To solve the problem in Example 7.27, enter the following keystrokes.

These keystrokes correspond to an annuity with 20 payments of $12,500,000 and a present value of $155,777,629. The calculator provides the solution of 5%. 

*GORDON, RAEDY, SANNELLA, 2019, INTERMEDIATE ACCOUNTING, 2ND ED., PP. 346-348*

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