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56

41. 42. 43. 44.

50m Chapter 9

1. 1.00

2. .82

3. 12.9%

4. 116.8%

5. ) $25,633

6. ) Option

7. 8.07%

8. $767.55

9. fl) 720

10. 13.89% . .00685

12. b) ) 1- -

13. ) 1,161,400

14. ) $141,500

15. 7.91%

16. ) $946.93

17. ) $857.33

18. 6.4646

19. ) 9.64%

20. 26.45%

21. Minimum = $128,614 Maximum = $129,470

b) $23,736 ) $16,658 b) Option

b) 240

<f) 1 - -"" b) 16,600 ) 1.11% b) $128,300

b) $1036.53 b) $1000.00

b) 10.51%

c) 7.975% rf) 7.953% /) Yes

(v + 2 2)

24. 25.

a(0 =

28. a) $3616

30. $1591 32.

33. a) (1) -1.8012 b) (1) 1.8854

34. a) 0 Z>) 94.307 35.

1250

b) 2.2035 c) 1.7628 d) .6046

*(0 = V (V + V)

(2) 0 (3) 1.8343 (2) 0 (3) -1.7531 c) 312.5

i(n + l)(n + 2)

36. 38.

$13,223 in 1-year zero coupon bonds $15,061 in 3-year zero coupon bonds $9624 in 5-year zero coupons bonds

39. $9091 in 1-year zero coupon bonds $8265 in 2-year zero coupon bonds $7513 in 3-year zero coupon bonds $6830 in 4-year zero coupon bonds $6209 in 5-year zero coupon bonds

40. a) $179.37 b) 12.01%

41. a) 0 < P] < .6980 b) No solution exists

42. a) .2186 < Pi< .5931 b) No solution exists

Chapter 10

3. a) 8% in all years b) 0 in year 1; .01 in year 2; .Olyin year 3

c) $1294.92 rf)$1224.94 e) $1259,71 f) $1259.82 g) 26.08

4. a) .07997 b) .79390 c) .16630 d) .( 735

5. mean = 2.5772

s.d. = .0169

6. a) mean = 1.823 b) mean = 14.121 c) = .549 d) mean = 7.298

s.d. = .058 s.d. = .297 s.d. = .017 s.d. = .134

40. $4.6!

$365.63

$116,500

31.33% 7 + 4



Svmbol

Section

Description

Symbol

Section

Description

accumulated value of a decreasing annuity

retrospective loan balance

10.4

a measure of equity required to support liabiUties

{+

flat price of a bond

e{t)

10.3

error term in AR(1) and AR(2) processes

m ,+

market price of a bond

10.5

exercise (striking) price of an option

10.5

value of a callable bond

10.2

expectation of random variable X

10.5

value of a noncallable bond

expected present value

convexity

project financing rate

redemption value of a bond

forward rate

10.5

value of a call

10.6

value of call if stock goes down

App. IV

probabihty density ftinction

fiinction being solved using iteration

contribution, deposit

face amount, par value of a bond

contribution, deposit at time /j.

present value of single payment at time n

redemption value of a serial bond

bond coupon

10.6

value of call if stock goes up

accrued bond coupon

summation of redemption values of serial bonds

Fix)

App. IV

cumulative distribution fiinction

cov[X, Y]

10.3

covariance of random variables X and

modified coupon rate on a bond

effective rate of discount

gix)

iteration formula

rate of simple discount

rate of compound discount

«1. 82

10.3

roots of die characteristic equation for die AR(2) process

factor in the declining balance method of depreciation

base amount of a bond

App. Ill

common difference in an arithmetic progression

factor in a variation of die declining balance mediod of

present value of level perpetuity starting at time n

depreciation

10.6

length of time interval in binomial lattice

duration, Macaulay duration

periodic charge of an asset

effective rate of discount from time n - 1 to

present value of increasing perpetuity starting at time

nominal rate of discount convertible mthly

effective rate of interest

rate of simple interest

10.5

constants in the Black-Scholes formula

rate of compound interest

sinking ftind deposit

yiekl rate, internal rate of relim

7.10

dividend on stock

investment rate when j is the reinvestment rate

D>

depreciation charge

interest rate on loan in sinkinj fiind method

annual percentage rate (APR)

Di,D2

day of date

nominal rate of interest

present value of a decreasing annuity



436 The Symbol

E, m,

«2

Pv Pi

10.2 10.2 10.2

2.3 various 10.5

7.4 9.5 10.6

9.10

10.5

P{i)

cumulative distribution fiinction for the standard normal distribution

premium or discount on a $1 bond

probabiUty bond does not default

probability of price increases in binomial lattice

probability bond does not default at time /

proportion of fiinds in different investments in asset/liability matching

price of a bond price of a put

price of a serial bond

summation of prices of serial bonds

amount of principal repaid on loan amount of principal adjustment on bond

instantaneous rate at which principal is being repaid

net present value

net present value based on spot rates probability bond defaults

expenses at setdement on real estate mortgage that must be reflected in APR

Symbol Section Description

..(m)

Sjt\

j(mi) S

5.9 project return rate

7.3 coupon rate on a bond

9.4 rate of inflation 10.4 yield rate in CAPM

App. ni common ratio in a geometric progression

10.4 return on equity

10.4 risk-free rate of interest

10.4 yield rate on a specific security

10.4 appropriate rate to discount liabilities

10.4 yield rate on die market portfolio

4.3 equivalent payment per interest conversion period

6.3 level installment payment to repay a loan

8.5 level periodic return

5.2 return, wididrawal

6.6 varying installment payments to repay a loan

9.9 net receipt in immunization

App. Ill sum of a progression

App. Vin sum of an annuity

1U.2 variance of rate of interest

9.10 wididrawal amounts at different times in asset/liability matching

accumulated value of an n-period

3.2 annuity-immediate

3.3 annuity-due

4.4 annuity-immediate payable mdily

4.4 annuity-due payable mdily

4.5 continuous annuity

App. Vin expected value of die sum of an annuity

8.5 salvage value of asset after depreciation

10.5 current stock price

8.4 sum of die first r positive integers

App. IX random variable for die value of an asset

Section Description

9.9 cash outflow generated by UabiUties

App. VIII first moment about the origin App. VIII second moment about the origin 10.2 first moment of 1 + j, about the origin

second moment of 1 + J, about the origin first moment of (1 + i,)" about the origin second moment of (1 + about the origin periodic maintenance expense month of date the term of a transaction



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