Image you are 30 years old and want to save money to meet the following three goals:
To save $150,000 in 5 years for the down payment to purchase a house, which is estimated to be $600,000. You will take a 30-year fixed rate mortgage at an APR of 5.5% for the remaining housing price.
To retire in 35 years, that is, when you are 65, and the money saved at that time is able to generate $18,000 each month for your 20 years of retirement living. Assuming you will withdraw the $18,000 at the beginning of each month.
To leave an inheritance of $1,000,000 to your kids after you leave this world, which is expected at the end of your 20-year retirement life.
You think you can afford to save $3000 at the end of each month during the following 5 years and then you will withdraw $150,000 from the saving and take the mortgage to buy the house. After buying the house, you will continue saving while paying the mortgage payment each MONTH until you retire at the age 65. You will pay off the mortgage loan when you retire.
Assume you can earn 10% EAR before you retire and 6.5% EAR after you retire.
Use the EAR to calculate the monthly interest rate you can earn before and after you retire, respectively. (6%)
What is the total retirement saving you must have on the day you retire so it can support your goals 2 and 3? (20%)
After paying the $150,000 down payment in 5 years, how much saving is remained in your account? (4%)
Draw the time line. Mark the month 0, 1, 59, 60, 61, 419, 420, 421, 659, 660 and specify the cash flow occurs at the end of that month. Note the sign of the cash flow: inflow (outflow) is positive (negative). (10%)
To achieve your goals, how much must you save at the end of each MONTH after you purchase the house until you retire? (30%)
What is your monthly mortgage payment? (10%)
Including the monthly mortgage payment, what is the total amount you need to set aside each month, that is, sum of your answer d and e? (10%)
You want to get an idea of how your purchasing power is affected by inflation after you retire. Assume the inflation rate stays at 3% over the following decades. What is the real value of the $18,000 in terms of purchasing power in 55 years? (10%)