【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)