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1. Future value (FV) of asingle cash flow
= PV × (1+r) n = PV × FVF r,
n
2. Future value of Annuity
= Annuity amount × [(1+r) n + 1] ÷ r
=
Annuity amount × FVAF r, n
3. Future value of Annuity
due = [Annuity amount × [(1+r) n + 1]
÷ r] × (1+r)
= Annuity amount × FVAF r, n × (1+r)
4. Present value (PV) of asingle cash flow = FV ÷ (1+r) n = FV × PVF r,
n
5. Present value (PV) ofAnnuity = Annuity amount × [1 – {1 ÷ (1 + r)
n}] ÷ r
= Annuity amount × PVAF r, n
6. Present value (PV) of
Annuity due = [Annuity amount × [1 – {1 ÷ (1 + r)
n}] ÷ r] × (1+r)
= Annuity amount × PVAF r, n × (1+r)
7. Present value of perpetuity = Cash flow ÷ r
8. Present value of growing perpetuity = Cash flow ÷ (r – g)
9. Present value of growing annuity = [Cash flow 1 ÷ (r-g) ] ×
[ 1- { (1+g) ÷(1+r)}n ]
10. Present value of growing annuity due = [Cash flow 1 ÷ (r-g) ] ×
[ 1- { (1+g) ÷ (1+r)}n ] × (1 + r)
11. Future value of growing annuity = Present value of growing annuity ×
(1+r) n
= [Cash flow 1 ÷ (r-g) ] × [ (1+r)n – (1+g)n]
12. Future value of growing annuity due = Present value of growing annuity ×
(1+r) n × (1 +r)
= [Cash flow 1 ÷ (r-g) ] × [ (1+r)n – (1+g)n]
× (1 +r)
In case, r = g
13. Present value of growingannuity = CF1 × [n ÷ (1 + r)]
14. Present value of growingannuity due = CF1 × [n ÷ (1 + r)] ×(1
+ r)
15. Future value of growingannuity = CF1 × n ×
(1+r) n−1
16. Future value of growingannuity due = CF1 × n ×
(1+r) n−1 × (1 + r)
Finding growth rates
FV = PV (1 +g) n
g (growth rate) = (FV/PV)
PVFr, n = PVIFr, n
=
Present value interest factor at rate of interest r after n periods.
PVFAr, n = PVIFAr, n
=
Present value interest factor for an annuity at rate of interest r after nperiods.
FVFr, n = FVIFr,n
= CVIPr,n = CVPr,n = Future or compound value interestfactor at rate of interest r after n periods.
FVFAr, n = FVIFAr, n
= CVIPAr, n = CVPAr, n = Future or compound value interestfactor for an annuity at rate of interest r after n periods.
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