常用公式大全form2(SOA北美精算师考试handbook notes)
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STA 4183 – The Theory of Interest
Formulas for Annuities
Annuities Present value Accumulated value Perpetuities Present value
Immediate
1− an| =
1 1+i
i
n
(1 + i)n − 1
sn| =
i
Due
1− a¨n| =
1 1+i
d
n
(1 + i)n − 1
s¨n| =
d
Immediate
1 a∞| = i
1
Due
a¨∞| = d
a¨n| = (1 + i)an|
a¨n| = an−1| + 1
n = − log(1 百度文库 ian|) log(1 + i)
1− i≈
an| 2 n
an|
s¨n| = (1 + i)sn| s¨n| = sn+1| − 1
n = log(1 + isn|) log(1 + i)
i≈
sn| n
2
−1
sn|
Formulas for Annuities
Annuities Present value Accumulated value Perpetuities Present value
Immediate
1− an| =
1 1+i
i
n
(1 + i)n − 1
sn| =
i
Due
1− a¨n| =
1 1+i
d
n
(1 + i)n − 1
s¨n| =
d
Immediate
1 a∞| = i
1
Due
a¨∞| = d
a¨n| = (1 + i)an|
a¨n| = an−1| + 1
n = − log(1 百度文库 ian|) log(1 + i)
1− i≈
an| 2 n
an|
s¨n| = (1 + i)sn| s¨n| = sn+1| − 1
n = log(1 + isn|) log(1 + i)
i≈
sn| n
2
−1
sn|