# 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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## 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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