1. Thomas wants to purchase a new house. It will cost $40,000 and he will finance it at an annual rate of 6% with monthly payments over 5 years. What will his loan balance be at the end of the first month after he has made his first payment? (this is also the balance at the start of the second month)

a. 39,333

b. 40,000

c. 39,427

2. You are trying to determine how much you need in order to retire comfortably. If you were to retire today, you could live on $8,000 per month. But you will retire in 30 years and with expected inflation of 3% per year, you want a starting monthly retirement income that will have the same purchasing power when you retire as $8,000 has now. You anticipate living for 25 years in retirement. The first retirement check will come at the end of your first month of retirement and all of the checks will be of the same size. You expect to earn 9% on your investments. You have already accumulated $40,000 in your retirement account. How much must you save at the end of each month between now and the day you retire, with your first savings deposit in one month, in order to fund your retirement?

a. $942.06

b. $1,179.89

c. $1,036.27

please show formulas if possible