Question

The Blue Shoppe has adopted a policy of increasing the annual dividend on its common stock at a constant rate of 1.65 percent annually. The firm just paid an annual dividend of $1.84. What will the dividend be eight years from now?

Answer 1

$2.10

Explanation:

The annual dividend will be increased at a constant rate of 1.65% annually.

Therefore:

Let $1.84 be this years payment

For next year, payment = $1.84+(1.65% of $1.84) = 101.65% of $1.84

When we have sequences in which the next term is gotten by multiplication by a constant factor or percentage, it is a Geometric Sequence.

nth term of a Geometric Sequence,
`U_n=ar^(n-1)`

First term, a=1.84

Common ration=101.65%=1.0165

n=8+1=9

`U_n=ar^(n-1)\\U_9=1.84 X 1.0165^(9-1)\\=1.84 X 1.0165^8\\=2.097`

The dividend 8 years from now will be $2.10.