Can you please show me your work please? Thank you!

1. a. You deposit $100 into an account earning a 10% annual rate of interest. How much money will you have in the account at the end of five years? (30 points) b. You have just won the lottery and have a choice of receiving a lump sum of $1,000,000 or an annuity of $100,000 per year for 15 years. If the appropriate discount rate is 8%, which alternative would you choose? (10 points) Explain. (30 points) c. What happens to the future value of a sum of money deposited for N years as the rate of return k increases? (15 points) What happens to the present value of a sum of money to be received at the end of N years as k increases? ( 15 points) 2. Applies TVM techniques using multiple compounding periods per year. a. You are saying for retirement and haye the opgortunity to invest in a security that pays a 12% annual rate of return, compounded quarterly. If you invest $100,000 in the security now how much will you have in your retirement account al the end of 10 years? b. Would it be better for your retirement account if the returns on the security were simply compounded once a ycar? (5 points) Fxplain why or why not. ( 15 points) Is more frequent compounding good for borrowers or for lenders and why? ( 30 points) c. Colin's grandparents want to make a gift of $50,000 towards his college education fund in 12 years. I Iow much money would they have to deposit today in an account that accrues interest monthly if the rate quoted by the bank is 6 percent? 3. Applies TVM techniques to real problems Peter is considering making a loan of $500,000 to Paul. It is a three-year loan with annual payments due at the end of each year and a 7% annual interest rate. Find the payments that would be required to amortize the loan over the threc-ycar period and then prepare an amortization schodule to demonstrate how the loan will he fully paid off in threc years