AB Inc is expected to pay dividends in year $1$ of $$2$ and starting in year $2$ there is an annual dividend of $$3$ growing at a rate of $2\%$ for the next $15$ years, and afterwards there are annual dividends of $54$ indefinitely growing at a rate of $3\%$ each year.

a$)$ If the market interest rate is $6\%,$ what is the price of the share today?

b$)$ If the market rate is $4\%$ in the first year and then $6\%$ in year $2$ and thereafter, what is the price of the share today.

c$)$ In general, if market interest rates decrease, what happens to the price of the share? Explain.