All of the following are conditions for an annuity, except for:

		Periodic cash flows must be equal in amount
		The time periods between the cash flows are the same length
		The interest rate is constant for each time period
		The interest rate is compounded at the middle of each time period

Lori Miller deposits $2,000 each year into a savings account beginning January 1, 2010. The last payment will be made on January 1, 2019, after which the total amount will be withdrawn to purchase a yacht. To find the amount available on January 1, 2019, after the last payment, Lori must determine:

		the present value of an ordinary annuity
		the present value of a single sum
		the future value of an ordinary annuity
		the future value of a single sum

The Smith Company desires to have on deposit $300,000 on January 2, 2023, to fund a major capital campaign beginning on that date. To accumulate the desired sum, Smith will make equal annual deposits on January 2, 2020, 2021, 2022 and 2023 in a fund that will earn 10% compounded annually. Smith must make four annual deposits of: (future value of an ordinary annuity of 10%, 4 periods is 4.64100, future value of 1 of 10%, 4 periods is 1.46410, and future value of an annuity due of 10% and 4 periods is 4.41632)

		$50,000
		$64,641
		$75,000
		$94,641

Using the table approach, the future amount of an annuity due may be calculated by finding the table factor for the future amount of an ordinary annuity of:

		n+1 rents and then subtract 1
		n+1 rents and then add 1
		n-1 rents and then add 1
		n-1 rents and then subtract 1