Index
A
accumulated value 298
future value of a constant-growth annuity 421
future value of a deferred annuity 409 future value of a general annuity due 371 future value of an ordinary general annuity
360
future value of an ordinary simple annuity 348
future value of a simple annuity due 365 future value of compound interest
calculations 302 addition 22. See also BEDMAS
addition principle 48
algebra 39. See also algebraic equations, algebraic expressions
algebraic equations 48–51 addition principle 48 definition 48 division principle 48 equivalent equations 48 multiplication principle 48 principle of equations 48–50 subtraction principle 48
writing equations in one variable 51 algebraic expressions
addition and subtraction 41 binomial 41
coefficient 40 constant 39 constant term 40 definition 39
division of monomials by monomials 43 evaluating expressions 41
expression 40
factoring expressions with common factors 44
factors 41 like terms 41 monomial 41 multiplication 42 polynomial 41 term 40
terminology used 40 trinomial 41 unlike terms 41 variable 39, 40 amortization
amortization schedule 431 amortization schedule
calculating the final payment 437 calculating the principal balance 435
interest portion 431 principal portion 431
amount credited 155. See also partial payments, cash discount
amount of periodic payment of an annuity 343. See also periodic payment annual salary 82. See also payroll annuity 343. See also ordinary annuity,
annuity due, other types of annuities types of annuities based on compounding
periods 345
types of annuities based on payment dates 344
annuity due 344. See also simple annuity due, general annuity due
calculating future value 365, 371 calculating nominal interest rate 387 calculating number of payments 381 calculating periodic interest rate 387 calculating periodic payment 377 calculating present value 365, 371 calculating time period 381 arithmetic 2. See also arithmetic mean,
arithmetic operations arithmetic mean 28 arithmetic operations 41
assessed value of a property 95. See also property taxes
averages
simple arithmetic average (arithmetic mean) 28–29
weighted average (weighted arithmetic mean) 32–33
B
base 69
logarithms with base 10 57 logarithms with base e 57 P, R, B triangle 70
BEDMAS 22. See also brackets, exponents, division, multiplication, addition, subtraction
binomial 41 bi-weekly salary 83
blended combination of the GST and PST. See also Harmonized Sales Tax (HST) bond 463
maturity date 464
purchase price 464, 465, 475 quoted Price 472
bond schedule 480
brackets 22. See also BEDMAS
break-even analysis 219. See also contribution
margin, cost-volume-profit analysis, loss, profit
break-even chart 244 break-even point 219, 221, 222 fixed costs 219
selling price 220 total costs 219 total revenue 220 total variable costs 219 variable costs 220 break-even chart 244 break-even point 219, 220 break-even price 164–165 break-even volume 232
C
calculator 222. See also Texas Instruments BAII Plus calculator
capital investments 497 Cartesian coordinate system 195 case studies
applying percentages in personal and business scenarios 101 applying ratios in business 134 borrowing and investing using simple
interest 293, 294
borrowing to start a business 339 cost-volume-profit analysis at a
manufacturing company 256 financial planning for a secure future 428 Financing a Growing Business 461 investing for the future 338 Lease or Finance Option 401 merchandising cycle of a product:
manufacturer to consumer 192 Raising Money Through Bonds 494 saving for retirement 400
cash discount 152–154 cash discount terms 154 end-of-month dating 154–155 ordinary dating 152–154 payment terms 152
receipt-of-goods dating 154–155 coefficient 40
commercial paper 286 maturity period 287 commissions 86–89
base salary + commission 86, 88 graduated (variable) commission 86, 87 quota then commission 86, 88 straight commission 86 common logarithms 57
compounding frequency 298, 343 compounding period 298
compound interest 297. See also Texas Instruments BAII Plus calculator amount of compound interest 298 compounding frequencies 299 compounding period 298 definition 297
difference from simple interest 297 effective interest rate 325
equivalent interest rates 328 equivalent payments 313 future value formula 298 interest upon interest 297 nominal interest rate 299
number of compounding periods 299 periodic interest rate 299, 319 present value formula 298 time period 300
constant-growth annuity 420 future value 421
ordinary simple constant-growth annuity 421
present value 421 constant growth rate 420 constant term 40
contribution margin 220. See also break-even analysis, cost-volume-profit analysis contribution ratio 221–231. See also break-
even analysis, cost-volume-profit analysis
cost 160 definition 161 fixed costs 219 net cost factor 142 rate of markup on cost 161 total costs 219
total variable costs 219 variable costs per unit 220 cost-volume-profit analysis 225. See
also break-even analysis graphical approach 244–248 coupon rate 464
currency appreciation and depreciation application of exchange rate fluctuation 126 currency conversion 119
buying and selling currencies 123 currency cross-rate table 119 exchange rates 119
proportions 112
currency cross-rate table 119
D
dating 154. See also cash discounts, ordinary dating, end-of-month dating, receipt-of-
goods dating
days-table 263. See also simple interest DCF. See discounted cash flow decimal 3
converting a decimal to a percentage 68 converting a percentage to a decimal 68 relationship among percentages, fractions,
and decimals 67
declining balance method 282. See also demand loan
deferred annuities 407 deferred period 407 future value 409 present value 409 demand loan 282
declining balance method 282–283 interest paid on a demand loan 272 partial payments 282
digit 2
discount 141. See also cash discount amount of markdown 169 amount of trade discount 142 cash discounts 152
markdown 168 rate of markdown 169 reduced profit 176 series of trade discounts 144
single equivalent trade discount rate 146 single trade discount 142
trade discounts 141 discounted cash flow 497 discounted value 298
present value of a constant-growth annuity 421
present value of a deferred annuity 409 present value of a general annuity due 371 present value of an ordinary general
annuity 360
present value of an ordinary perpetuity 416 present value of an ordinary simple annuity
353
present value of a perpetuity due 416 present value of a simple annuity due 366 present value of compound interest
calculations 309
discounting and proceeds 285–286 for interest-bearing note 286 for non-interest-bearing note 286
distribution chain 141. See also merchandising division 22. See also BEDMAS
dividing a polynomial by a monomial 43 division principle 48
due date 274, 275
Eeffective interest rate 325. See also compound interest
end-of-month dating 154 EOM (end-of-month) dating 154 equation 195
equivalent equation 48 linear equation 195
simple algebraic equations 48 equivalent equations 48 equivalent interest rate 328
equivalent nominal interest rate 329 equivalent periodic interest rate 329 equivalent payment 313. See also simple
interest, compound interest
of a series of payments in simple interest calculations 276
of a single payment in simple interest calculations 275
single payment equivalent to two payments in compound interest calculations 313
two equal payments equivalent to single payment in compound interest calculations 313
equivalent value 274 equivalent payments 274 exchange rates 119. See also currency
conversion
buying and selling currencies 123–125 currency appreciation 125–126 currency cross-rate table 119 currency depreciation 125–126 expanded form 2, 54
expert advice 404
understanding your investment options 404
exponents. See also BEDMAS
convert an exponential notation to a standard notation 24 exponent 1 25
exponential notation 24 fractional exponent 55 negative exponent 25 rules of exponents 54–55 zero exponent 25
expression 40. See also algebraic expressions
F
factors
common factors 14 composite numbers 11 highest common factor 14 lowest common denominator 13 multiples 10
prime numbers 11 final value 75
percent change 75
financial calculator 222. See also Texas Instruments BAII Plus calculator first degree algebraic equation. See also linear
equation fixed costs 219 focal date 276, 313
equivalent payment 276 formulas and their applications 60
definition 60 fractional exponent 55 fractions 15–19
arithmetic operations with fractions 18–20 comparing fractions 17
converting a fraction to an equivalent fraction 16
converting a fraction to a percentage 68, 77 converting an improper fraction into a
mixed number 16
converting a percentage to a fraction 67 converting a mixed number into an
improper fraction 16 definition 15
division of fractions 19
fraction in lowest (or simplest) terms 17 improper fraction 15
mixed number 15
multiplication of fractions 19 proper fraction 15
reciprocal of a fraction 15, 20, 23 reducing or simplifying a fraction 17 relationship among percentages, fractions,
and decimals 67 subtraction of fractions 18 types of fractions 15
whole number as a fraction 15
future value 298, 302, 343. See also compound interest, annuity, other types of annuities of a deferred annuity 409
of a simple annuity due 365 of a general annuity due 371 of an ordinary general annuity 360 of an ordinary simple annuity 348 of an ordinary simple constant-growth
annuity 421
G
general annuity due 345. See also annuity due definition 345
equivalent periodic interest rate 371 future value 371
nominal and periodic interest rates 388 periodic payment 378
present value 371
Goods and Services Tax (GST). See also sales taxes
graduated commission 86
graphical approach to CVP analysis 244 graphing linear equations 198
Gross Debt Service Ratio 450 gross pay 82
gross profit 161 grouping 41
Guaranteed Investment Certificate 281 non-redeemable GIC 281
redeemable GIC 281
H
highest common factor 14 hourly rate 82
hourly wages 89
I
improper fraction 15
converting a mixed number into an improper fraction 16
converting an improper fraction into a mixed number 16
initial value 74 percent change 74
interest 259, 343. See also simple interest, compound interest, annuity applications of simple interest 280 calculating the compound interest terms
300
compound interest 297 definition 259
effective interest rate 325 equivalent interest rates 328 equivalent nominal rate 329
equivalent periodic interest rate 329, 360 interest paid on a demand loan 272 interest rate 298
interest rate per compounding period 298 interest upon interest 297
nominal interest rate 299, 319, 384, 387 periodic interest rate 299, 319, 384, 387 simple interest 259
simple interest rate 260 time value of money 259
interest-bearing promissory note 283. See also promissory notes
internal rate of return 508 investment options 404–405
bonds 404
equity investments 404
Guaranteed Investment Certificate 404 investment plans 405
investment vehicles 404
mutual funds 404 RESP 405 RRSP 405 shares 404 Treasury Bills 404 IRR. See internal rate of return
L
least or lowest common multiple 11 legal due date 284
like terms 41
linear equation 195. See also rectangular coordinate system
consistent and inconsistent systems 206 dependent and independent equations 206 elimination method 210
graphing linear equations 198–203 substitution method 209
table of values 198
linear system 206. See also linear equation list price 141–142. See also trade discount logarithms
common logarithms (log) 57 natural logarithms (ln) 57–58 rules of logarithms 58
loss 175. See also break-even analysis, markdown
M
manufacturer’s suggested retail price (MSRP) 141
margin 161
markdown 169. See also merchandising calculation table
amount of markdown 169–170 rate of markdown 169–170 reduced selling price 168
markup 160–164. See also merchandising calculation table
amount of markup 161, 185, 237 gross profit 161
margin 161 rate of markup 161 rate of markup on cost 161 rate of markup on selling price 161 selling price 160
maturity date 284
maturity value 298. See also simple interest, compound interest
mean 28
merchandising 141
merchandising calculation table 162 merchandising chain 141
mill rate 96 mixed number 15
monomial 41 monthly salary 82 mortgage
closed mortgage 447 fixed rate mortgages 446 open mortgage 447 Variable rate mortgages 447 multiples 10
definition 10
lowest common multiple 11 multiplication 22. See also BEDMAS
multiplication principle 48
multiplying a monomial by a monomial 42 multiplying a polynomial by a monomial
42
multiplying a polynomial by a polynomial 43
N
natural logarithms 57 negative exponent 25 net cost factor 142 net income 220 net pay 82
net present value 503
net price 142–143. See also trade discount nominal interest rate 299, 319, 343 non-interest-bearing promissory note 285.
See also promissory notes
number of compounding periods 298, 322
O
operating profit 161 order of operations 22–26
BEDMAS 22
calculator method to find exponent 26 exponential notation 24–26
signed numbers 23
ordered pairs of numbers. See also linear system
ordinary annuity 343, 344, 345. See also ordinary simple annuity, ordinary general annuity
calculating future value 348, 360 calculating nominal interest rate 387 calculating number of payments 381 calculating periodic interest rate 387 calculating periodic payment 377 calculating present value 353, 360 calculating time period 381 ordinary dating 154
ordinary general annuity 345. See also ordinary annuity definition 345
equivalent periodic interest rate 360
future value 360
number of compounding periods 360 periodic payment 378
present value 360
ordinary simple annuity. See also ordinary annuity
definition 345 future value 348
nominal and periodic interest rates 388 periodic payment 377
present value 353 origin 195
other types of annuities 406. See also deferred annuities, perpetuity, constant-growth annuity
overhead expenses 161 overtime factor 82 overtime pay 85 overtime rate 82
P
partial payments 155–156. See also cash discount
amount credited 156 two partial payments 156 payback period 511
pay for pay period 83, 185, 237
payment terms. See also ordinary dating, End- Of-Month dating, Receipt-Of-Month dating
pay period 82
payroll. See also commissions annual salary 82 definition 82 gross pay 82 hourly rate 82 hourly wages 89–90 net pay 82
overtime factor 85–86 overtime rate 85 pay period 82
piecework rate 82, 90–91 percent 67
percentages 67–72
converting a decimal to a percentage 68 converting a percentage to a decimal 68 converting a percentage to a fraction 67–68 definition 67
P, R, B triangle 70
rate, portion, and base 69–72
relationship among percentages, fractions, and decimals 67
percent change 74–81 definition 74 periodic cost 487
periodic interest rate 299, 319, 384, 387
periodic payment 377. See also annuity perpetuity
ordinary perpetuity 416 perpetuity due 416 present value 416 piecework rate 82, 90 place value 2–3
definition 2 expanded form 2, 3 of decimal numbers 3 of whole numbers 2 standard form 2, 3 word form 2, 3 polynomial 41 portion 69
P, R, B triangle 70 power of a power 54 power of a product 54 power of a quotient 54
pre-programmed calculator 222. See also Texas Instruments BAII Plus calculator
present value 298, 309, 343. See
also compound interest, annuity, other types of annuities
a general annuity due 371
formula for compound interest calculations 298
of a general deferred annuity due 410 of a general perpetuity due 417 of an ordinary general annuity 360 of an ordinary general perpetuity 418 of an ordinary perpetuity 416 of an ordinary simple annuity 353 of an ordinary simple constant-growth
annuity 421
of an ordinary simple deferred annuity 409 of an ordinary simple perpetuity 417 of a simple annuity due 366 principal amount 298 principle of equations 48 product rule 54
profit (net income) 220. See also break-even analysis, markup
promissory notes 283 face value 284
interest-bearing promissory note 283 maker 283
maturity date 283
non-interest-bearing promissory note 285 payee 283
term 283
property taxes 95–96
assessed value of a property 95 mill rate 96–97
proportions 112–116
pro-ration 116–117 prospective method 435
Q
quadrants 196. See also linear equation quota then commission 86, 88 quotient 16, 39, 51, 55 quotient rule 54, 58
R
rate 69, 110 P, R, B triangle 70 unit rate 110 ratio 105–109
comparing quantities of items that have different kinds of measure 107 comparing quantities of items that have the
same kind of measure 107–108 equivalent ratio 105
expressing a ratio of more than two quantities 105
expressing a ratio of two quantities 105 order of a ratio 107
reducing a ratio to its lowest terms 105 reducing ratios to an equivalent ratio whose
smallest term is one 106 sharing quantities using ratios 108–109 terms of a ratio 105
ratio-proportion method 70 receipt-of-goods dating 154
rectangular coordinate system 195. See also linear equation
Cartesian coordinate system 195 quadrants 196
sign convention 195 terminology 195 x-coordinate 196 x-intercept 199 y-intercept 199
reduced profit 175. See also markdown reduced selling price 168. See also markdown repeating decimals 72
retrospective method 435
return on investment. See internal rate of return
R.O.G. (receipt-of-goods) dating 154 ROI. See Internal Rate of Return rounding 4–5
decimals 5, 6 definition 4 percentages 7 rules for rounding 5 whole numbers 4, 5
S
sale price 175 sales taxes 93–96 savings account 281 selling price 160 semi-monthly salary 82 simple algebraic equations 48
simple annuity due 345. See also annuity due definition 345
future value 365 present value 366 simple arithmetic average 28 simple interest 259
maturity value 268 principal 260 p, r, t triangle 269 simple interest rate 260 time period 260 sinking fund 484
slope 199. See also rectangular coordinate system, linear equation
standard form 2 standard notation 24 statutory holiday 90 straight commission 86 subtraction. See also BEDMAS
subtraction principle 48
T
taxes 93–98. See also property taxes, sales taxes
term deposits 281 term of an annuity 343
Texas Instruments BAII Plus calculator cash-flow sign convention 303
end-of-period or beginning-of-period 350 exponent 26
future value of a general annuity due 371 future value of an ordinary general annuity
361
natural logarithm 57 nominal interest rate 320
number of days in a time period 265 number of decimals to 9 350
present value of an ordinary simple annuity 354
present value of a simple annuity due 368 TVM row description 303
Using the Amortization Worksheet in the BAII Plus Financial Calculator 435 time period 259, 322, 381
time period in days between dates 262 time value of money 259
total costs 219
total debt service ratio 450 total revenue 220 total variable costs 219
trade discount 141. See also list price, net price amount of trade discount 142
net cost factor 142 series of trade discounts 144 single equivalent trade discount rate
146–147
single trade discount 142 treasury bills 286
denominations 286 trinomial 41
U
unit rate 110 unlike terms 41
V
variable commission 87 variable costs per unit 220
W
wages 89 weekly salary 83 weighted average 32 whole number 2 word form 2 word problems 40 workweek 82
X
X-axis. See also graphical approach to CVP analysis, graphing linear equations rectangular coordinate system 195 x-coordinates 195
Y
Y-axis. See also graphical approach to CVP analysis, graphing linear equations rectangular coordinate system 195 y-coordinate 195
yearly salary 82
Z
zero as an exponent 54 zero as a power 58
