Beginning from a steady state in the Solow growth model, which of the following does not occur when there is an increase in the saving rate?

A$.$ An increase in the saving rate will cause a permanent increase in the growth rate of capital.

B$.$ In the new steady state, investment will equal depreciation and no additional rise in capital per worker will occur.

C$.$ If the saving rate increases, a larger portion of the present output per worker will be invested in new capital.

D$.$ The level of output per worker will increase from its current level.