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Contemporary Mathematics

# Formula Review

## 6.2Discounts, Markups, and Sales Tax

$discount=percent discount×original pricediscount=percent discount×original price$

$sale price=original price-discountsale price=original price-discount$

$sale price=original price-percent discount×original price=original price×(1-percent discount)sale price=original price-percent discount×original price=original price×(1-percent discount)$

$markup=percent markup×costmarkup=percent markup×cost$

$retail price=cost+markupretail price=cost+markup$

$retail price=cost+percent markup×cost=cost×(1+percent markup)retail price=cost+percent markup×cost=cost×(1+percent markup)$

$sales tax=purchase price×tax ratesales tax=purchase price×tax rate$

$Total price=purchase price+purchase price×tax rate=purchase price×(1+tax rate)Total price=purchase price+purchase price×tax rate=purchase price×(1+tax rate)$

## 6.3Simple Interest

$I=P×r×tI=P×r×t$

$T=P+IT=P+I$

$T=P+P×r×tT=P+P×r×t$

$I=P×r365×tI=P×r365×t$

$FV=P+I=P+P×r×tFV=P+I=P+P×r×t$

$A=P×r×(1+r)t(1+r)t−1A=P×r×(1+r)t(1+r)t−1$

$PV=FV(1+rt)PV=FV(1+rt)$

## 6.4Compound Interest

$A=P(1+rn)ntA=P(1+rn)nt$

$PV=A(1+rn)n×tPV=A(1+rn)n×t$

$Y=(1+rn)n-1Y=(1+rn)n-1$

## 6.6Methods of Savings

$A=P(1+rn)ntA=P(1+rn)nt$

$ROI=FV-PPROI=FV-PP$

$FV=pmt×(1+r/n)n×t-1r/nFV=pmt×(1+r/n)n×t-1r/n$

$pmt=FV×(r/n)(1+r/n)n×t-1pmt=FV×(r/n)(1+r/n)n×t-1$

## 6.7Investments

$annual return=(FVP)(1t)-1annual return=(FVP)(1t)-1$

$P/E=Share PriceDividendP/E=Share PriceDividend$

$Yld%=Annual DividendShare Price×100%Yld%=Annual DividendShare Price×100%$

## 6.8The Basics of Loans

$I=P×rnI=P×rn$

$pmt=P×(r/n)×(1+r/n)n×t(1+r/n)n×t−1pmt=P×(r/n)×(1+r/n)n×t(1+r/n)n×t−1$

## 6.9Understanding Student Loans

$funding gap=total cost−all aidfunding gap=total cost−all aid$

$A=P(1+rn)ntA=P(1+rn)nt$

$pmt=P×(r/n)×(1+r/n)n×t(1+r/n)n×t−1pmt=P×(r/n)×(1+r/n)n×t(1+r/n)n×t−1$

$discretionary income=gross income−1.5×poverty guidelinediscretionary income=gross income−1.5×poverty guideline$

## 6.10Credit Cards

$I=ADB×r×d365I=ADB×r×d365$

## 6.11Buying or Leasing a Car

$pmt=P×(r/n)×(1+r/n)n×t(1+r/n)n×t−1pmt=P×(r/n)×(1+r/n)n×t(1+r/n)n×t−1$

$MD=P−RnMD=P−Rn$

$APR=2400×MFAPR=2400×MF$

$MF=APR/2,400MF=APR/2,400$

$PMT=(P−R)n+(P+R)×MFPMT=(P−R)n+(P+R)×MF$

## 6.12Renting and Homeownership

$pmt=P×(r/12)×(1+r/12)12×t(1+r/12)12×t−1pmt=P×(r/12)×(1+r/12)12×t(1+r/12)12×t−1$

$T=pmt×12×tT=pmt×12×t$

$CoF=T−PCoF=T−P$

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