$4.$ Expected dividends as a basis for stock values

The following graph shows the value of a stock$$s dividends over time. The stock$$s current dividend is $$1\mathrm{.}00$ per share, and dividends are expected to grow at a constant rate of $3\mathrm{.}50\%$ per year. The intrinsic value of a stock should equal the sum of the present value $($PV$)$ of all of the dividends that a stock is supposed to pay in the future, but many people find it difficult to imagine adding up an infinite number of dividends.

Calculate the present value $($PV$)$ of the dividend paid today $($D$)$ and the discounted value of the dividends expected to be paid $10,20,$ and $50$ years from now $($D$10,$ D$20,$ D$50$

$).$ Assume that the stock$$s required return $($rs

$)$ is $10\mathrm{.}40\%.$

Note: Carry and round the calculations to four decimal places.