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$1.$ The Cowboy Sweepstakes has just informed you that you have won $$100,000.$ Instead of receiving the lump sum option, you have chosen the annuity payout option and the amount is to be paid out at the rate of $$10,000$ a year for the next $10$ years. With a discount rate of $9$ percent, what is the present value of your winnings of the annuity payout option?

$2.$ What would your investment account be worth in $10$ years if you currently have $$8,000$ saved and plan to add $$165$ per month at the end of the month for the $10$ years if the account pays $9\mathrm{.}5\%$ interest compounded monthly?

$3.$ At a growth $($interest$)$ rate of $7\mathrm{.}8$ percent annually, how long will it take for you to triple your money?

$4.$ What is the future value of an $$3,095$ annuity payment over $10$ years if the interest rates are $6$ percent?

$5.$ What is the present value of a $$8,400$ annuity payment over $5$ years if interest rates are $5\mathrm{.}5$ percent?

$6.$ Suppose that you place $$7,000$ in a bank account each year for the next $20$ years. How much would be in your bank account at the end of the twentieth year if the deposits earned an annual rate of return of $5\%$ each year?

$7.$ Repeat above question for annuity due.

$8.$ If you want to accumulate $$90,000$ and you have $$9,000$ saved now, how many years will it take if you pay $$100$ per quarter and your investment account pays $6\mathrm{.}5\%$ compounded quarterly?

$9.$ What is the present value of a $$150,000$ cash flow to be received at the end of each of the next $10$ years from an account that earns an annual rate of $6\mathrm{.}5\%?$

$10.$ Repeat above question for annuity due.

$11.$ What is the future value of an ordinary annuity of $$62,000$ for $4$ years, if interest rates are $6$ percent?

$12.$ What is the future value of the same annuity due?

$13.$ What is the present value of a $$310,000$ cash flow to be received at the end of each of the next $15$ years from an account that earns an annual rate of $9\%?$

$14.$ What is the present value of an annual payments of $$1,500$ discounted back $9$ years at an annual rate of return of $3\%?$

$15.$ What is the future value of a series of $$35,600$ quarterly payments received at the end of each quarter for the next $7$ years if invested at an annual rate of return of $7\mathrm{.}5\%$ compounded quarterly?

$16.$ Repeat above question for annuity due? $($paymens received at the beginning of each quarter$).$

$17.$ Jake$$s Used Cars just sold you a clunker $($you need it to get to class on time$).$ You financed the $$36,000$ purchase price for $48$ months. They said your payment would be $$890.$ What interest rate did they charge you $($assume monthly compounding$)?$

$18.$ Geegee checks Daniel$$s credit rating and determines that he will qualify for a $7\mathrm{.}8\%$ auto loan, and they agree that his trade$-$in is worth $$7,500.$ The cost of the car is $$37,900.$ If he is planning to finance the loan for $4$ years, how much does he have to pay every month?