Problem 54.8 Calculate the modified duration of an annuity due with payments of 100 for 10 years using an interest rate of 8%.

An investment in a new handling equipment would cost $84,248 and save $20,000 per year for 5 years. What is the nominal annual interest rate earned in this investment?

. A geotechnical engineering firm has been awarded a job to design the foundation of an office building. The project is postponed and will not start for four more years. The firm needs to estimate the present worth of the costs of the project. At the year four, the cost will be $175,000 decreasing by $50,000 per year for the next three years. If the interest rate is 4%, what is the present worth of the projected cost of the project?

A town want to replace an existing bridge that cost $5000 annually in an operation and maintenance has a remaining useful life of 20yrs. The new bridge will cost $500000 for construction and an additional $2000 for manual operation. The new bridge is expected to have a useful life of 50yrs. Thus, extending the life by 30yrs if interest rate is 8% single payment present worth of 20yrs is what?