Please solve all of the time value of money questions below using the BA II Plus calculator.

$1.$ You have $$6,000$ to invest. You can earn interest at an annual rate of $9\%.$ How much money will you have at the end of $5$ years? Remember to round your final result to two decimal places.

$fill in the blank $1$

$9,231\mathrm{.}74$

$2.$ Imagine you win lottery! You have two options for receiving your prize:

A$.$ Lump sum: take a one$-$time payment of $$15$ million.

B$.$ Annuity: Receive $$1$ million at the end of the year per year for $15$ years, guaranteed by the lottery commission.

The annual interest rate is $7\%.$

What is the present value of the lump sum option?

$fill in the blank $2$

$15,000,000$

What is the present value of the annuity option? Round your answer to the nearest whole number.

$fill in the blank $3$

$4,491,244\mathrm{.}33$

Which option is better? fill in the blank $4$

A

$3.$ You wish to spend $$12,000$ on a vacation $4$ years from now. You can invest your money at an annual interest rate of $9\%.$ How much do you need to save per month in order to reach your $$12,000$ goal? Round your answer to two decimal places.

$fill in the blank $5$

$111,556\mathrm{.}18$

$4.$ Your firm issues bonds payable with a $$1,500,000$ face value and a $8-$year life at a $12\%$ annual interest rate. They pay interest semi$-$annually. At the time they are sold, the market expects a $10\%$ rate of interest, so they sell for a premium.

Determine the semi$-$annual interest payment.

$fill in the blank $6$

$90,000$

Determine the present value for the annuity. Round your answer to two decimal places.

$fill in the blank $7$

$980,896\mathrm{.}60$

Determine the present value of the future payment of $$1,500,000$ at maturity. Round your answer to two decimal places.

$fill in the blank $8$

$1,662,566\mathrm{.}54$

Determine the present value of bonds payable. Round your answer to two decimal places.

$fill in the blank $9$

$1,662,566\mathrm{.}54$