Consider the case of the following annuities, and the need to compute either their expected rate of return or duration.

James inherited an annuity worth $$2,735\mathrm{.}54$ from his uncle. The annuity will pay him three equal payments of $$1,100$ at the end of each year. The annuity fund is offering a return of $.$

James$$s friend, Chris, wants to go to business school. While his father will share some of the expenses, Chris still needs to put in the rest on his own. But Chris has no money saved for it yet. According to his calculations, it will cost him $$21,421$ to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $$3,800$ at the end of every year in a mutual fund, from which he expects to earn a fixed $6\%$ rate of return. It will take approximately years for Chris to save enough money to go to business school.