49. Little Tim Scrooge is anxious to attend college. In fact, he intends to go to Podunk U. (a.k.a. PU) when he is old enough and will stay for 6 years after which he will have his MBA. His father, Ebenezer, is sympathetic with Tim's aspirations, but he believes Tim must take care of him first. Therefore, Ebenezer will finance Tim's education with a bequest at his death and until that time Tim is to look after his father. PU will cost $15,000 a year for the six years (payable at the beginning of each year) and Ebenezer specifies in his will that at his death the necessary funds will be deposited in an account paying 10% annually. Ebenezer will retire 20 years before his death and during his retirement he wants to have $100,000 per year (end of year). The funds necessary for Little Tim's education as well as Eb's retirement pay will come from an amount he will have accumulated during his working years which will also be invested at 10% over his retirement years. Ebenezer planned to accumulate the necessary funds in two ways: (Assume 30 working years) 1) He owned 500 shares of IBM stock at the beginning of his working years that had a $100 per share market value. He believed that this price should increase at a 3% annual rate and he would sell the stock in 30 years. Further, he expected a $4 per share dividend each year (end of year) and he believed he could invest these proceeds at an 8% rate. 2) He would put aside $2,000 per year (end of year) in an IRA which he would withdraw at the end of his working period (ignore taxes). a. What annual rate must Ebenezer earn on the IRA account in order to carry out his plans? 12.33% b. Suppose Ebenezer accumulated the appropriate amount of funds at the beginning of his retirement years, but upon retirement he withdraws $10,000 for a trip abroad. He carries out the rest of the plan ($100,000 a year and the balance to Little Tim), how much will Little Tim owe the bank upon graduation if he borrows at a 6% rate to finance all costs not covered by Ebenezer's bequest (he will borrow the money as he needs it, i.e., at the beginning of each year)? $104,401.09 49. Little Tim Scrooge is anxious to attend college. In fact, he intends to go to Podunk U. (a.k.a. PU) when he is old enough and will stay for 6 years after which he will have his MBA. His father, Ebenezer, is sympathetic with Tim's aspirations, but he believes Tim must take care of him first. Therefore, Ebenezer will finance Tim's education with a bequest at his death and until that time Tim is to look after his father. PU will cost $15,000 a year for the six years (payable at the beginning of each year) and Ebenezer specifies in his will that at his death the necessary funds will be deposited in an account paying 10% annually. Ebenezer will retire 20 years before his death and during his retirement he wants to have $100,000 per year (end of year). The funds necessary for Little Tim's education as well as Eb's retirement pay will come from an amount he will have accumulated during his working years which will also be invested at 10% over his retirement years. Ebenezer planned to accumulate the necessary funds in two ways: (Assume 30 working years) 1) He owned 500 shares of IBM stock at the beginning of his working years that had a $100 per share market value. He believed that this price should increase at a 3% annual rate and he would sell the stock in 30 years. Further, he expected a $4 per share dividend each year (end of year) and he believed he could invest these proceeds at an 8% rate. 2) He would put aside $2,000 per year (end of year) in an IRA which he would withdraw at the end of his working period (ignore taxes). a. What annual rate must Ebenezer earn on the IRA account in order to carry out his plans? 12.33% b. Suppose Ebenezer accumulated the appropriate amount of funds at the beginning of his retirement years, but upon retirement he withdraws $10,000 for a trip abroad. He carries out the rest of the plan ($100,000 a year and the balance to Little Tim), how much will Little Tim owe the bank upon graduation if he borrows at a 6% rate to finance all costs not covered by Ebenezer's bequest (he will borrow the money as he needs it, i.e., at the beginning of each year)? $104,401.09
