### Examples - Determining i or n for Known Cash Flow Values

**EXAMPLE**

If Laurel made a $30,000 investment in a friend’s business and received $50,000 5 years later, determine the rate of return.

**Solution**

Since only single amounts are involved, i can be determined directly from the P/F factor.

Alternatively, the interest rate can be found by setting up the standard P/F relation, solving for the factor value, and interpolating in the tables.

From the interest tables, a P/F factor of 0.6000 for n = 5 lies between 10% and 11%. Interpolate between these two values to obtain i = 10.76%.

**EXAMPLE**

Pyramid Energy requires that for each of its offshore wind power generators $5000 per year be placed into a capital reserve fund to cover unexpected major rework on field equipment. In one case, $5000 was deposited for 15 years and covered a rework costing $100,000 in year 15. What rate of return did this practice provide to the company?

**Solution**

The cash flow diagram is shown in Figure 2–24 . Either the A/F or F/A factor can be used. Using A/F,

From the A /F interest tables for 15 years, the value 0.0500 lies between 3% and 4%. By interpolation, i = 3.98%.

Figure 2–24 Diagram to determine the rate of return |

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