$4)$

a$)$ Calculate the future value in $6$ years of $$1000$ today with annual compounding and a $6\%$

semi$-$annual interest rate.

b$)$ Suppose someone saves $$10000$ today and will have $$11000$ one year from today. If

compounding is quarterly, what must be the interest rate on this account?

c$)$ Suppose there is a current cash flow of $$8$ that is expected to grow by $16\%$ each year. If

the annual interest rate is $20\%,$ what is the present value of this stream of future cash

flows?

d$)$ Using the information from part c$),$ what would be the future value of that same stream of

cash $2$ and a half years from now if compounding is annual and $20\%$ annual interest?

e$)$ Suppose the present value of a growing perpetuity is $$1050.$ If the annual interest rate is

$10\%,$ and the current cash flow is $$50,$ what must be the growth rate of this perpetuity?