By the end of 2020, both Steve and Helen, a married couple, will be 30 years old. Further, they are expecting their son to be born in the latter half of December 2020. Steve and Helen are both employed and their pre-tax annual income is $75,000 and $60,000, respectively. Their combined federal and state income tax rate is 28%.

They plan to buy their own house. Actually, they have already looked around and houses they like in their area sell for $300,000. To get a mortgage loan to buy the house, the down payment is 10% of the house price, while the closing costs are two percent of the loan amount. Since they have no savings currently, they would like to save the money required for the down payment and the closing costs during 2021 and then buy their house at the beginning of 2022. At the end of each month they can put the money they will be saving in 2021 towards the down payment and the closing costs in a bank account paying an annual interest rate of one percent compounded monthly. They know that 30-year mortgage loans carry a three and a half percent annual interest rate and require payments at the end of each month.

Steve and Helen also want to save money for their sons college education. They are aware that the average annual cost of college is currently $35,000, it increases by four percent each year, and college lasts for four years. Starting January 31, 2021, at the end of each month they will deposit an equal amount in their sons college fund account until his eighteenth birthday month, and they expect the annual interest rate on these savings to be five percent compounded monthly. Their sons college tuition will be due at the beginning of each of the four years; the first tuition is due in 2038.

Steve and Helen want to retire when they turn 65 and have enough savings by then to last them until they turn 80. In the first year of their retirement they would like to have as much after-tax annual income as they currently have; however, they would like their after-tax annual income to increase by two percent annually for the remaining 14 years of their retirement. Starting January 31, 2021, they plan to save an equal amount at the end of each month until they turn 65; they expect their savings to earn an annual interest rate of five percent compounded monthly between now and the time they turn 80. When they retire, Steve and Helen will be receiving their annual income at the end of each retirement year.

1. Calculated the amount of money Steve and Helen have to save each month in 2021 to have enough money by December 31, 2021 to cover the down payment and the closing costs for their new house. Also, calculate how much they will pay in interest in the first six months of their mortgage loan. Finally calculate the balance of their mortgage loan at the end of June 2022.
2. Calculated the amount of money Steve and Helen have to deposit each month in their sons college fund account.

3. Calculated the amount of money Steve and Helen have to save each month to reach their retirement goal