【CFA】時間価値

1.How to calculate Future Value of Annuity (FVOA)?

1.1 What is Annutiy? "Recurring investement"

1.2 What is FVOA?

⇔How much will a number of investement be worth at the end of time period in the future?

Time        0 1 2  3      ・・・・・                                 F                       

Payment  X X X X      ・・・・・      　　　　　　　  X

*Interest=i

FVOA=X(1+i)^1+X(1+i)^2+X(1+i)^3+..........+X(1+i)^n-1+X(1+i)^n

FVOA=X(1-(1+i)^n)/(1-(1+i) 

FVOA=X((1+i)^n-1)/i

Ref) Sum of Geomtric Progression

Sn=   A+Ar + Ar^2+.............+Ar^n-1

rSn=   　Ar+.........................+Ar^n-1+Ar^n

(1-r)Sn=A-Ar^n

Sn=A(1-r^n)/(1-r) 

2.How to calculate Present Value of Annutiy (PVOA)?

⇔How much is a number of investement be worth at the begging of time period in the presence?

Time        P 1 2  3      ・・・・・                                 F                       

Payment  X X X X      ・・・・・      　　　　　　　  X

*Interest=i

PVOA=X(1+i)^-1+X(1+i)^-2+X(1+i)^-3+..........+X(1+i)^-(n-1)+X(1+i)^-n

PVOA=X(1+i)^-1【｛(1+i)^-1｝^n-1】/【｛(1+i)｝^-1】-1

PVOA=X(1+i)^-1【｛(1+i)^-1｝^n-1】/【｛(1+i)｝^-1】-1　×(1+i)/(1+i)