1. Alex's grandmother has $12,000 in a bank account that is not earning interest. Alex is 12 years old, and his grandmother has promised to give him this $12,000 to spend on college tuition - once he graduates from high school in six years. Alex understands the time value of money, so he wants to persuade his grandmother to put the money in an S&P index fund instead. Although no one can be sure what the rate of return will be, historically S&P funds have earned an average of 10% per year. Calculate the future value of the $12,000 (in six years) if the money was invested at a 10% annual return instead. Assume compounding is only once a year.
2. Sofia has a government bond that will be worth $1000 when it matures in 5 years. She wants to sell it to her brother because she needs the cash now for car repairs. Assuming an interest rate of 5% and assuming monthly compounding, what is the present value of the bond?
3. Sam and Nadia just inherited $160,000 from Nadia's grandmother. This is exactly the amount of principal remaining on their mortgage. They are wondering: Should they pay off the mortgage or keep making their monthly payments and invest the money in an S&P Index fund? They have a 30-year mortgage at 3% interest, and they have 16 years remaining to pay. They pay $1000/month in principal and interest payments. Assume they could earn about 6% annual interest on an investment, which would compound monthly.