A municipality has just completed the construction of a bridge. It was calculated that operating and maintenance (O&M)costs of this bridge will be $20 000 in the first year with a 5% increase each year thereafter for the next 4 years. The interest rate used in calculations was 7.5% per year. What interest rate should be used to calculate the present worth of O&M costs over 5 years if we use the geometric series to present worth conversion factor?

Question

Quizplus · Accepted Answer

The correct interest rate to use for calculating the present worth of O&M costs over 5 years, when the costs increase by a fixed percentage each year (5% in this case) and the calculations are based on a geometric series to present worth conversion factor, is found by adjusting the nominal interest rate (7.5%) for the growth rate of the costs (5%). This adjusted rate is called the "real" interest rate and can be calculated using the formula $i_{real} = \frac{1 + i_{nominal}}{1 + g} - 1$, where $i_{nominal}$ is the nominal interest rate and $g$ is the growth rate. Plugging in the given values: $i_{real} = \frac{1 + 0.075}{1 + 0.05} - 1 = \frac{1.075}{1.05} - 1 = 0.0238$ or 2.4% when rounded to the nearest tenth.

A Municipality Has Just Completed the Construction of a Bridge