$4.$ If Jackson deposits $$80$ at the end of each month in a savings account earning interest at a rate of $2\%/$year compounded monthly, how much will he have on deposit in his savings account at the end of $2$ years, assuming he makes no withdrawals during that period? $($Round your answer to the nearest cent.$)5.$Luis has $$190,000$ in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to "roll over" his assets to a new account. Luis also plans to put $$2000/$quarter into the new account until his retirement $20$ years from now. If the new account earns interest at the rate of $2\mathrm{.}5\%/$year compounded quarterly, how much will Luis have in his account at the time of his retirement? $($Round your answer to the nearest cent.$)$$ $6.$ The Pirerras are planning to go to Europe $4$ years from now and have agreed to set aside $$150/$month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of $2\%/$year compounded monthly, how much money will be in their travel fund at the end of the fourth year? $($Round your answer to the nearest cent.$)$$ $7.$ Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r$\%/$year compounded m times a year. $($Round your answer to the nearest cent.$)$S $=130,000,$ r $=6\mathrm{.}5,$ t $=25,$ m $=128.$ Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of $5\mathrm{.}5\%/$year compounded monthly. If the future value of the annuity after $13$ years is $$65,000,$ what was the size of each payment? $($Round your answer to the nearest cent.$)$$ $9.$ The management of Gibraltar Brokerage Services anticipates a capital expenditure of $$24,000$ in $3$ years for the purchase of new computers and has decided to set up a sinking fund to finance this purchase. If the fund earns interest at the rate of $2\%/$year compounded quarterly, determine the size of each $($equal$)$ quarterly installment that should be deposited in the fund. $($Round your answer to the nearest cent.$)$$ $10.$Andrea, a self$-$employed individual, wishes to accumulate a retirement fund of $$450,000.$ How much should she deposit each month into her retirement account, which pays interest at a rate of $5\mathrm{.}5\%/$year compounded monthly, to reach her goal upon retirement $45$ years from now? $($Round your answer to the nearest cent.$)11.$ Since he was $21$ years old, Ben has been depositing $$275$ at the end of each month into a tax$-$free retirement account earning interest at the rate of $5\mathrm{.}5\%/$year compounded monthly. Larry, who is the same age as Ben, decided to open a tax$-$free retirement account $5$ years after Ben opened his. If Larry's account earns interest at the same rate as Ben's, determine how much Larry should deposit each month into his account so that both men will have the same amount of money in their accounts at age $65.($Round your answer to the nearest cent.$)12.$The Cooper Foundation contributes $$40,000$ per year into an annuity fund for building a new zoo. The fund earns $6\mathrm{.}5\%$ interest. Find the amount in the fund at the end of $15$ years. $($Round your final answer to two decimal places.$)13.$How much should a family deposit at the end of every $6$ months in order to have $$4000$ at the end of $5$ years? The account pays $4\mathrm{.}7\%$ interest compounded semiannually. $($Round your final answer to two decimal places.$)$