5) One standard assumption for annuities and gradients is A) each payment occurs at the beginning of the period

Q) Ans:-

Step1)

An annuity can be defined as equal payment series over an equal period sequence. In other words, Annuity is a particular amount of money deposited in an account each year for a particular period of time. In the case of an ordinary annuity, each payment occurs at the end of the period, and in the case of annuity due, each payment occurs at the beginning of the period.

A Gradient can be defined as a series of cash flow which rises or falls by a certain amount or percentage each year. The increase and decrease in the cash flow are fixed and constant either in the percentage form or in the constant value form. In this type of series, every year, the cash flow at the end is different.

Step2)

Option A is incorrect as in annuity the payment can be made either at the beginning or at the end of the period.

Options B and C are also incorrect because the payments made in gradient is different in each year because of its uniform increase. Thus, neither in the beginning not in the end annuities and gradients coincide.

Option D is also incorrect. Hence, The correct answer is Option 'E' that is the one standard assumption of annuity and gradient is that the payment period and the compounding periods are the same because if payment period and compounding periods are different than it will not be possible to apply these formulas in any of the cases. If these are different than we have to calculate the effective rate of interest to get the correct answer. Therefore, it is a standard assumption that payment periods and compounding periods are the same.

Step3)

Correct option is the E.