John is about to have his first child when his daughter turns $18$ he would like to buy her an annuity that pays $$4000$ every six months for four years if they annuity he considers pays $5\%$ compounded semi annually find the present value of this annuity what monthly payments would he need to make into a savings plan paying $5\%$ compound monthly if he saved for the full $18$ years Mary is considering retirement in $20$ years she decides she would like to buy an annuity that would pay her property taxes for $15$ years after her retirement her property tax bill is $$2000$ paid annually if she found an account that paid $3\%$ compounded annually what annual payments would you like to make an order to meet her goals