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Unformatted text preview: 1. Suppose someone offered you your choice of two equally risky annuities, each paying
$5,000 per year for 5 years. One is an annuity due, while the other is an ordinary annuity. If you are a rational wealth maximizing investor, which annuity would you
choose? @The annuity due. b) The ordinary annuity. c) Either one, because as the problem is set up, they have the same present value. (1) Without information about the appropriate interest rate, we cannot ﬁnd the values of
the two annuities, hence we cannot tell which is better. e) The annuity due; however, if the payments on both were doubled to $10,000, the
ordinary annuity would be preferred. 2. Assume you can invest to earn a stated annual rate of return of 12 percent, but where
interest is compounded semiannually. If you make 20 consecutive semiannual
deposits of $500 each, with the ﬁrst deposit being magic todayigvhat will your balance be at the end of Year 20? (I) ' [g I r Hgﬁfﬂffi/r' a) $52,821.19 500500 “’—« ' 50g... ’55 7 b) $57,900.83 . ,L 2o , Z, c $58,988.19 500 (1+ 2) "‘ (1w: = 02,524.178v
$62,527.48 . ‘2’ 2— e) $64,131.50 (21) 3. You are currently at time period 0 (today), and you will receive the ﬁrst payment on
an annual payment annuity of $100 in perpetuity at the end of this year. Six full years
from now you will receive the ﬁrst payment on an additional $150 in‘perpetuity, and
at the end of time period 10 you will receive the ﬁrst payment on an additional $200
in perpetuity. If you require a 10 percent rate of return, what is the value today of these perpetuities? O
3) $2,349.50 i '00 r , w 100 ,. , . loo—‘9 00
b) $3,226.85 ISO , ,, 2 ’50 90
c $ , 85.42 200. .900
2,779.58
e) $2,975.40 ‘ .
(DO , 15‘0 ,.,.._
"s ‘0 J .0 71.0.) < 'T ‘1' 1 *5" '00 i” 5744.261 4. Josh and John are each trying to save enough money to buy their own cars. Josh is
planning to save $100 from every paycheck (he is paid ever 2 weeks.) John plans to
put aside $150 each but month but has already saved $1,500. Interest rates are
currently quoted at 10 percent APR. Josh’s bank compounds interest every two
weeks while J ohn’s bank compounds interest monthly. At the end of 2 years they
will each spend all their savings on a car (i.e., they each buy a car). What is the price
of the most expensive car purchased? Johﬂ w,
a $5,744.29 (1 +"3Y ~l .5 27’
$5797.63 150 ‘7' 4— I500 (1+ 7;)
c $5,807.48 "9)
(1) $5,703.02 .—1 e) None of the answers above is correct. 57 017. (—53 5. Your family purchased a house three years ago. When you bought the house you
ﬁnanced it with a $160,000 mortgage with an 8.5% nominal interest rate
(compounded monthly). The mortgage was for 15 years. What is the remaining
balance on your mortgage today? Assume you just made your 36th payment. _ .1— .__ .
a) $95,649 KOO/000 : Pin/WK I (1+ “9% m
b) $103,300 95:)
c $125745 .   — 4—, l2.
. ’, me ~ lb 75.38 V I ’ m4
, ‘ ' i 3.; ,
1 1575.58 (1+3: = HMO/34.04
(’32:) 6. Your client has been offered a 5year, $1,000 par value bond with a 10 percent annual
coupon rate. Interest on this bond is paid quarterly. If your client is‘ito earn a nominal
annual rate of return of 12 percent, compounded quarterly, how much should she pay for the bond? ‘ l 20 IO
 .1). OK?)
332 as C H Tﬂ + AL)”
2.. '.L T
$1,025 ———
:1; $1,216 < L’ )
e) $981 N 925101 1 2. 3 it 5‘ 51.9w ‘7
l————l———'r———l———+—_f———1‘—’—" 225_ 2.2.3] 3 3 3' 7. McPherson Enterprises is planning to pay a dividend of $2.25 per share at the end of
the year. The company is planning to pay the same dividend each of the following 2
years and will then increase the dividend to $3.00 for the subsequent 2 years. After
that time the dividends will grow at a constant rate of 5 percent per year. If the
required return on the company’s common stock is 11 percent per year, what is the
current stock price? . _._L_ '
$5250 225“ I  ("l—“03 + "5—11 +i—‘i‘5‘ a)  H (1.11) (L115 b $37.50 .
$40.41 ’ __
$50.00 3 . )‘3 > e) $32.94 + H — 0‘? LID)“ \
ll 8. Club Auto Parts just paid a dividend of $0.50, and the company expects to experience
no growth for the next 2 years. However, Club will grow at an annual rate of 5
percent in the third and fourth years, and, beginning with the ﬁfth year, it should
attain a 10 percent growth rate which it will sustain thereafter. Club has a required
rate of return of 12 percent. What should be the pricze per syarg of Club stock at the 00
‘> end of the second year? 5 S". ‘i (07. 79
a ,$<" «5‘3 5 .5511? . we
a) $19.98 $6) 4‘ v if _6og321
b) $31.21 5 , (egoc‘sn‘
c) $19.48 . 2‘ sym’ “0.2 __.s + b . A on) (1131+ A (1.1132 ~25?” 9. You have been offered a project paying $300 at the beginning of each year for the
next 20 years. What is the maximum amount of money you would invest in this project if you expect a 9 percent rate of return on yqur investment? v . g _ m
a $2,738.70 300 $2.985m3 0..., 4' 300
0) $15,347.70 (‘ 1— d) $6,000.00
6) $3,277.44 = 2 ‘3 8 5. o 3
10. The market price of outstanding bond issues often varies from face value because a) the maturity date has changed. )4 the coupon rate has changed.
the required rate of return has changed. (1) old bonds must sell for less than new bonds.
e) None of the above are correct. ...
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 Spring '10
 RAYMOND
 Time Value Of Money, Interest

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