1.You just won $1 million dollars in the lottery! They offer you two options for your winnings: a lump sum payment right now, or $100,000 a year over the next 10 years. Current 10-year interest rates are at 5%, and the current tax on lottery winnings is 40%.

What is the amount you will receive today with the lump sum option?

2.When we talk about marginal cost and marginal benefit/cost, why does the equilibrium point is the most convenient for the production of a product. If the marginal cost and the marginal benefit/revenue are the same Wouldn't the cost of producing a product would be the same as the revenue you obtain from selling it? Wouldn't you be earring nothing when you reach the equilibrium point?Extra question; Are marginal benefit and marginal revenue the same concept?

3.Calculate the amount of money you have at the end of the indicate a time. You've invest $3000 in an account that pays simple interest of 3% for 20 years.

4.If 3000 dollars is invested atinterest, find the value of the investment at the end of 6 years if interest is compoundeda) annuallyb) quarterlyc) monthlyd) continuously

5.In [Half of a Coin: Negative Probabilities](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.592.2043&rep=rep1&type=pdf), the author mentions bond duration.Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is $v = \\frac{1}{1+i}$ where $i$ is effective interest rate. Then the bond value today is given by$$B = \\sum_{t=1}^{n} R_tv^t$$The bond duration is$$D = \\frac{\\sum_{t=1}^{n} tR_tv^t}{\\sum_{t=1}^{n} R_tv^t}$$It can be seen that $$D = E[T]$$where$T$ is a random variable with range $t = 1,2,...,n$ each having probability $\\frac{R_t v^t}{B}$The author says something like we can have negative probabilities if we have negative $R_t$'s. So this is a kind of bond where instead of making a payment we get a certain amount of money? Is there such a thing? Or is that only in theory?

6.the principal p is brrowed and the loans future value a at time t is given. determine the loans simple interest rate r to the nearest tenth of percent. p=6000,a=6420,t=1year

7.Sean invested $3,000 into two accounts. One account paid 4% interest and the other paid 8% interest. He earned 5% interest on the total investment. How much money did he put in each account?

8.You are applying for an 80/20 mortgage to buy a house costing $175,000. The first (80%) mortgage has an interest rate of 4.75%, and the second (20%) mortgage has an interest rate of 7.525%. Both the first mortgage and the second mortgage are 30-year fixed-rate mortgages. What will the total amount of the mortgage be?

9.Why do companies is on cash while they have debt

10.$4000 is deposited in an account that pays an APR of 7.7% compounded annually. How long will it take for the balance to reach $100, 000?

It will take years for the balance to reach

$100,000.