Alysha has been offered two perpetuities: Grow and Shrink. Grow promises her $$200$ in one year and an annual cash flow that will

increase by $4$ percent per year forever. Shrink, in contrast, promises her $$1,900$ in one year but the annual cash flow will decline by $2$

percent forever. If her opportunity cost is $6$ percent per year and both annuities cost $$1,900,$ which annuity offers her the greater

value? $($Round "Shrink cost" to $2$ decimal places, e$.$g$.125\mathrm{.}12$ and other answer to $0$ decimal places, e$.$g$.12,512)$

Grow exceeds the cost by

Shrink exceeds the cost by

offers the greater value.