Key Formulas · Slater/Wittry, Math for Business and Finance: An Algebraic Approach
rorlion Formula (p. 75)
"x, -
laie x Base = Ponion
1
Current price
rice relative = _ _ __:._ _
B ase year' s price
r
x 100
This line
is called
the d1v1d111g
line
(p. 137)
pcscribing Data
I
Portion
• ~1--~- \ Base
/ ' '
of
s
e_
u_
_ o_f _al_l _v a_l_;_
Mean = _S_u_m
Number of values
j)
.,,
Rate
-
Amount
financed
Total of all
monthly payments
Total finance charge
interest charge
Total of all
Deferred payment price = monthly payments
Dow n
APR
=
72 X I
-----
(p. 257)
3P( N + I )+ l (N - I )
PY( i )
I
M onthly payment= PMT =
1-
Sum of products
.
WeIghted mean = - - - - - - --
+ Amount financed/Number of payments of loan
Add-on M ethod: Finance charge
Highest data point + Lowest data point in class
.
.
Midpoint= - -- - ' - - -- ,--- - _:___ _
(p. 259)
( 1 + i)'
(p. 139)
Sum of frequencies
Cash + Purchases _ Payments
Daily _ Previous +
advances
balance
balance
Median=
Step 1. Arrange values from smallest to largest in an ordered array.
Step 2. Find the middle value.
a. Odd number of values: Median is the middle value. You find this by first d ividing the total number of numbers by 2 . The next-higher number is the median.
b. Even number of values: Median is the average of the two middle values. (p. 140)
Average daily balance =
Sum of cumulative daily balances
# of days of the bill_ing cycle
Range = Highest value - Lowest value (p. 142)
I:(X - X)'
(p. 143)
_
Sample variance = s2 =
Net price= List price - Trade discount amount
Net price
.
List price =
Complement of trade discount rate
I:(X - 11)'
N
Population variance = a' =
Single equivalent discount = I - Net price equivalent rate
Population slll!)dard deviation= a=
~
(p. 283)
(p. 286)
(p. 287)
(p. 288)
(p. 288)
Panial payment
Amount credited = I - Discount rate
(p. 144)
~
Net price = List price (I - SEO)
(p. 144)
(p. 288)
(p. 299
Basic Retail Equation
I Selling price (S) =
Cost (C) + Markup (M)
(p. 3 18)
Markup Based on Cost Formulas
Calculating Pay
l,
(p. 282)
Trade discount amount = List price x Single equivalent discount
x)'
(p. 144)
Normal distribution
x Trade discount rate
Net price= List price x Net price equivalent rate
(p. 143)
(p. 265)
Trade Discounts
Trade discount amount= Lisi price
1
(p. 265)
x Average daily balance
Finance charge= Rate per month
Mode = value/s that occurs most often in a set
ofnumbers (p. 141)
Sample standard deviation= s =
(p. 261)
Cr edit Card Daily Bal ance (p. 265)
(p. 139)
2
I:(.r -
(p. 257)
+ payment
1
(p. 138)
11
(p. 256)
Gross pay= Hours employee worked
x
Rate per hour
(p. 189)
%MU (R) =
Hourly overtime p ay rate = Regular hourly pay rate + Ove rtime rate
Gross pay= Number of units produced
x Rate
(p. 319)
(p. 189)
Selling price = Cost
(8 )
(P)
(p. 189)
per unit
Dollar markup (P)
.
Cost (8 )
Taxable Income (p. 197)
x (I +
Percent markup on cost)
(R)
Se lling pric e (P)
Cost (8) = - - - - -- - - - -1 + Pe rcent markup o n cost (R)
Taxable income = Adjusted gross income - Standard or itemized deductions
- Exemption allowance
(p. 320)
(p. 32 1)
Markup Based on Selling Price Formulas
Sales Tax
Total sales
Actual sales = - - - - 1 + Tax rate
(p. 2 15)
%MU (R)
J'roperly Tax
Assessed value = A ssessment rate
x
Budget nee ded
Tax rate = Total assessed value
Various rate forms:
Cost
(P)
(p. 2 17)
Selling
price
(8)
Percent marku_p)
(
x
(p. 325)
I - on selling p rice
(p. 326)
(R)
Converting Percent Markup on Cost to Percent Markup on Selling Price
(p. 218)
3. Per $1,000:
1. Pe rcent x A ssessed value
Assessed value
2 Pe r $100: - - -- - x Rate
$100
.
(p. 324)
Selling price (8)
Cost (P)
Selling price (8) = - - -- - - --'--' - - - - - -- ! - Pe rcent markup on selling price (R)
(p. 2 17)
Market value
Dollar markup'(P)
=- - - - -
Assessed value
$,
1000
4. Mills: Mills x .001
x Rate
x Assessed value
Percent markup on co st
(p. 327)
I + Pe rcent mark up o n co st
Converting Percent Markup on Selling Price to Percent Markup on Cost
Pe rcen t markup on selling p rice
Total property
tax due
Tax rate
(Rate
Portion
I - Pe rcent markup on selling p rice
Total assessed
X
(p. 21 8)
value
Retail Equations
Base
Markdown pe rcent =
Risk Management
Coverage desired
$ l ,OOO
Life insurance premium =
Insured value
Fire premium = - -- - - x Rate
$100
(p. 327)
x Rate
(p. 230)
(p. 235)
Dollar markdow~
Selling price (original)
Selling price of perishables =
Total dollar sales
Number of units produced - Spo ilage
Con tribution margin (CM) = Selling price (S) - Variable cost (VC )
nslallmcnt BuJ·ing
Amount financed = Cash price - Down payment
(p.331 1
(p. 256)
Breakeven point (BE) =
Fixed co sts (FC)
Contribution margin (CM)
(p. 33-1)
(p. 331)
(p. 334)
lu.:,_,ic Babrncr Sbtc"1 • unnub
S,mple interest (I) = Ptindpal CPI :x Ra1e Ul/
As= = Uabd,ues + Ov,ner's equrty
I
(p. 3S4/
Exact number of days
llnrome St.aterr11m1
'-et 1orome = ~cnut:5 - & ~
Net sales = Gross sales -
( p. 360J
I
Sales rewrns
- Sales discounts
and allowances
I
Gross profit
N
Cost of merchandise
= et saes
I
from sales
(goods) sold
nme =
Rate=
I
I
Interest
Pnnclpal /. TJtTJe
I
I
(p
.u2,
(p. 4331
Ip. 4331
lp.435J
Ip. 435J
lnte<£<St
Time (in years) =
(p. 364 )
frend Aoal}sl~
Pnnclpal X Rate
l
(p. 4361
Simplr lm;o,unt S ou,
Each item
83."' amoum
iEach number nprcsse.(! as a percent of the base year.
(p. 366)
Bank dl5COUnt = Matuf'lt'/ value x Dr;count rate x T,me
l
Maturrty value = Face value
= 1Aatu(1ty value - Bank disa:>unt
Proceeds
I
(p. 3671
I
Formula
Ratio
Current assets
Current ratio
Current fiabilitles
Acid test (quidc ratio)
Top of fraction often ➔
referred to as quick asse-t:s
I
Current assets
- Inventory
- Prepaid e,,.penses
I
Current liabilities
I
P, = M(t - DT)
I
Ip. 4541
(p. 4591
Desired proceed:, =
P,
1 -DT
I
Ip. 4YJJ
Bank
Bank
because it may not be easy to convert the5': to cash.)
Accounts receivable
Average day's
coflection
Interest
Etfectr, e P.ate = - - - - -Proceed:. x nme
(p. 4531
tlumbef of dir/ S bank Wails
tor nole IO come duo;
X
=MIIY
360
~.,count rate
cfiscount
Onventory and prepaid e,-.penses are e-,,duded
(pp. 4-(J>-461I
} fo rtgago,,
(Ne~les )
~=
PV/iJ
<p. 4n,
T oti1l debt to
total assets
Tat.al liabilities
Return on
equity
Net income
Stockholde<s· equity
(1 fix momb =P Y R Y / )
2
Asset
turnover
Net sales
Total assets
UUTmt
Arr.onu.2000 ,;chedule:
princiP2! = principal
Profit margin
on net sales
Net income
Net sales
Compouodlng periods= Ye2n x Pmock per year
Total assets
I
1- - -
" + ;,•
Pri~ = .M,;JOlhly _ ~
redu,ajr,n
paymmt
S~A'
C,,mp,,und
Depreciation
Straight fine depredation expense =
Cost - Residual value
each year
Estimated useful rife in years
I
Depreciauon =
Cost - Residual value
per unit
Tat.al estimated units produced
Depredation eY.pense = Book val ue of equipment x Oep,eciation
rate
each year
at beginning of year
I
(p. 5(JJ1
Ip. 502)
Compound ilureR = Fuwre value - P r - value
Ip. 38SJ
(p. 5031
Fuwre value= PV/l + if
Interest for 11 <:?Jr
lp. 506/
P(inapal
FV
'I
Cost of goods
Cost of ending _ Cost of
available for sale inventory
- goods sold
I
Etfear,e rate (AP'fJ =
I
lnH'nwry Calculauons
Ip
lnlffm
I
I
o(
- Rcductir,o
princiP2!
l.ola-N rail! per period = .Sominal me/Period• per year l p.5W J
(p. 390)
Depredation amount = Unit depredation x Units produced
II
l
360
Interest
Principal = Rate y Tune
Ip. 363/
(p. 3641
I
Net income = Gross profrt - Operating e7.penses
365
& .act number of days
(p. 3631
Cost of
Net purchases
merchanch-.e = Beginning +
(purchases less
- Ending
(goods) sold
,nvento<y
returns and d iscounts) invenwry
!Ratio Anal,.,.;,.
-
Tune=
/ 1""'2 CT)
l'reseo& value = - - (p. 5/F)J
(p. 3901
(I
Anoujties
(p. 391 )
FV
(p. 407)
•
=PMT [' ' +i)'
. - ']
I
PV . =PMT
Cost of goods availab le at cost
Ending
Retail Method: Cost of goods available at retail x inventory al retail
+ i)'
I
[• --· ]
( I + i,.
-i --
Suwng fund Payment
(p. 412J
FV..,. =Pm'[
(I .._ i)' -
(p. 5291
i
I]
(I
+ i) I p. 53
( p. 5341
FV ..(i)
(I+ ir - I
{p. 538)
S1.ocks. Bonds. and l tuwal Fun<b
Beg.
Net
Gross Profit method: inv. + purchases
-
Estimated
Estimated
cost of = ending
inventory
goods sold
(p. 4131
Cost of goods sold
Net sales
Inventory Turnover at relailat cost: Average inventory or A,erage inventory
at retail
al
Beginning iment.ocy + Ending irr, ernory
1-.verage irr1ent0Cl/ =
2
cost
(p. 4151
(p.414)
I
Stock
I
Earnings per share = Closing pr,ce + Price earning rauo
I
Oo-~ pr'i ce pee share of stoct,;
PE ratio= - Annual earm195 pe.- share
I
I
Annual di'✓ldend per share
yiad - Toda/s dosing price per share
Yeatt-1 Ullefest
Bond yiekJ
Simple J.n lfftSI
Maturity value (MV) = Pr'JrJOpal (P)
+ Interest {I)
l
Ip. 432)
NAV=
MV= PO + RT1 ( p. 4321
I
Ip. 5591
I
Ip. 5591
l p. 559J
'
= Face 1alue of bof>d x 5'aled 1eafl1 ilr'.&r
Total annual in!efest o! bond
= Total wsrent co.st o1 bond a, do<,..ng
Cuuent market , a11,e c1 fi.;oo s .,,,~-ms
--
I
Ip. 5631
I
Ip 5631
- Cu
--I lumber Gf sna:es ~~"!:..~-c rr,
l p. 5(,<