Question

A payment system starts with an initial payment of $50 at the end of year 1, $52.8 at the end of year 2, and a payment of $ 55.7568 at the end of year 3. This payment system follows ..........................

   A.  
Either ( Arithmetic ) or ( geometric )

    B.  
Neither ( Arithmetic ) nor ( geometric )

    C.  
Arithmetic Gradients

    D.  
a geometric gradient

Answer 1

The payment at the end of Year 1 is $50.

The payment at the end of year 2 is $52.8

The payment at the end of Year 3 is $55.7568

From Year 1 to Year 2, payment increases by $2.8.

From Year 2 to Year 3, payment increases by $2.9568

The payment is not increasing by uniform amount.

So, the payment system does not follow arithmetic gradient.

Calculate percentage increase in payment between Year 1 and Year 2 -

Percentage increase = [(52.8 - 50)/50] * 100 = 5.6%

Calculate percentage increase in payment between Year 2 and Year 3 -

Percentage increase = [(55.7568 - 52.8)/52.8] * 100 = 5.6%

It can be seen that payment is increasing by a constant percentage each year.

When cash flow is increasing at constant percentage each year, the cash flow series follows geometric gradient.

Thus,

This payment system follows geometric gradient.

Hence, the correct answer is the option (D).