Case: The Case of the Almost Identical Twins
Once upon a time twin boys were born into a typical Ozian family. The boys, named Spender and Saver, were alike in every respect except the one indicated by their names. While they were in high school, both worked at part-time jobs earning the minimum wage of $4.445 per hour for the maximum hours permitted by law, viz., 44 hours per month. There was no income tax in Oz. Spender found many things on which to spend all of his income, while Saver arranged with his parents to add his monthly income to their money market fund which earned 8% per annum, compounded monthly.
At the end of four years of high school, each of the boys bought a car costing the amount of Saver's accumulated savings, which he withdrew from his parents' money market account to pay for the car. Spender financed his car on a "no money down," 18% per annum, compounded monthly contract for 48 months. Thus, during four years of university, both boys had cars, both spent the same amounts on other things, but Saver invested each month an amount equal to what Spender was paying on his car, the saving again being at 8% per annum, compounded monthly. Both boys financed their expenses while at the university in the same way: partly by working and partly with help from their parents.
When they graduated from the university, the two men continued their identical spending patterns, except that Saver was able to buy a home, using the accumulation of his savings from avoiding car payments in the previous four years as the down payment (20% of the purchase price), financing the remainder on a 10% fixed rate mortgage, payable monthly over 30 years. Spender rented a similar home, paying (the first year) "net rent" equal to Saver's monthly mortgage payments. Spender's lease also required that he reimburse his landlord for property taxes and insurance on the rental unit-amounts equal to Saver's costs for those items. Thus, Spender continued his pattern of spending all of his income, while Saver paid off his mortgage over 30 years.
Unfortunately for Spender, his "net rent" increased at the rate of 5% per annum, so his housing costs escalated considerably over the 30 years. In the meantime, Saver invested the difference between Spender's escalating "net rent" and his own fixed mortgage payment. Each year he accumulated the monthly saving in his 8% money market fund, then at the end of the year invested in a mortgage bond mutual fund yielding the same rate as he was paying on his own mortgage: 10% per annum, compounded monthly. His investments and earnings in that fund continued to compound over the remaining life of his own mortgage.
Upon "burning his mortgage" at the end of 30 years, Saver, now 52 years of age, let his accumulated investment in the mortgage bond mutual fund continue to earn interest for two years but did not add to it. Instead, he departed from his brother's spending pattern by adding consumption expenditures equal to what Spender was paying in "net rent." Two years later (age 54) Saver retired to Eve off the income earned on his mortgage bond mutual fund, but kept the level of principal unchanged for the rest of his life, leaving it to his heirs. Spender, alas, was in a different position. What does the future hold for him?
REQUIREMENTS:
1) Specific calculations to be made; please describe any shortcuts or approximations you use:
a) How much did each lad spend on his car upon graduating from high school?
b) How much did Saver pay down on his home? What was the total purchase price?
c) What were Saver's monthly mortgage payments?
2) What annual income did Saver have from age 54 until his death?
3) Describe the differences between Spender's and Saver's consumption expenditures over the several segments of their lives and the positions of their heirs upon their deaths.
4) Which bits of information given, or assumptions made, do you regard as unrealistic on the basis of your own experience? Roughly speaking (or precisely, if you wish), how would the results be affected by substituting your more realistic calculations?