Question

1. A payment system starts with an initial payment of $40 at the end of year 1, $42.8 at the end of year 2, and a payment of $45.60 at the end of year 3. This payment system follows ...............................

	A.	Either (geometric) or ( Arithmetic )
	B.	a geometric gradient
	C.	Neither ( geometric ) nor ( Arithmetic  )
	D.	Arithmetic Gradients

Answer 1

Geometric gradient and arithmetic gradient refer to the mathematical measurement for calculating the change in the value of cash flow weather increasing or decreasing. Geometric gradient shows the constant proportionate change in the cash value using ratio while arithmetic gradient explains the change in the cash flow by a constant value.

Here, the cash flow is given as $40, $42.8, $45.6….

For arithmetic gradient,

The difference between 1^st and 2^nd value is  

Similarly, the difference between 2^nd and 3^rd value is

Here, the difference between cash flow of each period is constant, which implies that the payment system follows arithmetic gradient.

For geometric gradient,

The ratio between 1^st and 2^nd value is

Similarly, the ratio between 2^nd and 3^rd value is

Here, the ratio between cash flow of each period is not constant, which implies that the payment system does not follow geometric gradient.

Hence, the correct option is D. Arithmetic Gradient.