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