Assume you have won a lottery prize of $$5,000,$ which works out great since you want to buy a new gaming PC that costs $$5,500.$ You decide to save the lottery winnings for one year by purchasing a bank CD with one year until maturity. The interest rate on your deposit is $12\%$ and inflation is expected to be $8\%$ over the next year. You plan to work part$-$time to make up any shortfall in your savings covering the cost of the gaming PC one year from now.

a$.$ How much money will you have in your bank account at the end of one year?

b$.$ What is the real interest rate you expect to earn on your deposit over the next year?

c$.$ Will you have enough money from the savings to buy the PC next year?

d$.$ If your answer to c$.$ is no$,$ how many hours of work @ $$\frac{15}{?}$ hour will be required to make up the shortfall?