12 - Question and Problem Answers Chapter 12 - Prices and...

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C (1 r ) 2 n 1 r $30,000 (1.03) 8 1 0.03 $266,770.08 Question and Problem Answers page 1 Chapter 12 - Prices and Yields ± 12 - 1: A. The answer to this question depends on how frequently the interest is compounded. If the bank compounds interest semi-annually (like the bond JQ is considering as the alternate investment) then at the end of four years JQ will have in his account $1,000,000(1.03)8 = $1,266,770.08 0 1yr 2yrs 3yrs 4 yrs $1,000,000.00 $1,030,000.00 $1,060,900.00 $1,092,727.00 $1,125,508.81 $1,159,274.07 $1,194,052.29 $1,229,873.86 $1,266,770.08 B. Under the same assumptions if JQ withdraws $30,000.00 every six months he will reduce the balance in his account to $1,000,000 each time he makes a withdrawal. The account earns interest, but it never earns interest on interest because JQ withdraws the interest before the new compounding period. At the end of four years JQ has generated a cash flow of $30,000. Every six months and still has his principal of $1,000,000 on deposit. This is the same cash flow and principal pattern in the four year 6% semi-annual Discovery Café bond. 0 1yr 2yrs 3yrs 4 yrs $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 C. If JQ buys the bond and deposits the coupon payments in the bank account then at the end of four years he receives a principal payment of $1,000,000.00 and the final coupon payment of $30,000.00 from the bond. He also has accumulated a total of $236,770.08 in his bank account for a total of $1,266,770.08. This is the same amount as if he had put the $1,000,000.00 in the bank account and allowed the interest to compound semi-annually. 0 1yr 2yrs 3yrs 4 yrs $1,000,000.00 $1,000,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 Account: $30,900.00 $62,727.00 $95,508.81 $129,274.07 $164,052.30 $199,873.87 $236,770.08 $1,266,770.08 Note that the total interest and interest-on-interest is calculated
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2F INANCIAL MARKETS .
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This note was uploaded on 08/25/2009 for the course FIN 300 taught by Professor Jackson during the Spring '07 term at University of Illinois at Urbana–Champaign.

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12 - Question and Problem Answers Chapter 12 - Prices and...

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