Finance-Crib Sheet

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Investment w/o Risk:
Inflowoutflow-1>r
R=Δpp0+cfp0
PV:V0=Vt1+kt=Vt*PVIF(k;t)
FV: Vt=V0*1+kt=V0*FVIF(k;t)
keffective=kstatedm, k stated over year:APR
Gross Interest Rate: 1+k
Going from one EAR to other: 1+kx month eff.yx-1=[1+ky month eff.] Compounded to EAR … use this… also, less than a year to annual (special case): EAR=1+kstatedmm-1 EPR=1+APRmmt
Continuous Compounding: Vt=etkc--- if the $ is received in one year then the formula is: V0=e-tkc, t-years and not periods and kc-discount Rate Relation between EAR and kC:kEAR=ekC-1 , kC=ln⁡(1+kEAR)

Present/future Value Additives: Cash flows at a particular time. Invest:NPV>0 Present Value of Annuities: V0=CF1- 11+knk=CF[PVIFAk;n] =
Present Value of Perpetuities:V0=CFk
1k=PVIFAk,n≡Annuity, n→∞
Future Values of Annuities:Vn=V0*FVIFk,n=CF*PVIFAk;n*FVIFk;n=CF*FVIFA(k;n) FVIFAk;n=1+kn-1k
Annuities Due: PVIFAduek;n=1-11+knk(1+k), FVIFAduek;n=1+kn-1k(1+k) Growing Annuity:V0=CF1*1-1+gn1+knk-g≡Annuity at g=0, CF2=CF1(1+g) Growing Perpetuity:V0=CF1k-g≡Prep at g=0
Amortized Loans: V0=CF*PVIFA(k;n)
Loan=Payment*PVIFA(k;n)
Canadian Mortgage: k1 Month eff.Rate=1+k216
Sample Mean: x=i=1nxin n
Risk or variability(s-variance):s2=i=1n((xi-x))^2 (n-1)
S=s2
EX=i=1mprobi*xi
Legend: R-Return, cf=Capital Gain, k=interest rate/year PVIFA: present value interest factor of annuity, m-Com. freq:#times/yr-given by question, k(EAR)-Affected due to compounding of interest rate, t-# of years, n-period, s2:Sample Variance, s:Standard deviation, m:number of different possible rationalization
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