1
ETC2430 Actuarial Statistics
Lecture Notes Week 4
Valuing Cashflows
1.
Valuing cashflows
Consider times t
1
and t
2
, where t
2
is greater than t
1
.
Since t
1
< t
2
, the discounted value at time t
1
of
C
due at
time t
2
is:
𝐶?𝑥𝑝 [− ∫
𝛿(?)??
?
2
?
1
]
Since:
∫
𝛿(?)??
?
2
?
1
= ∫
𝛿(?)??
?
2
0
− ∫
𝛿(?)??
?
1
0
And given that
𝑣(?) = ?𝑥𝑝 (− ∫ 𝛿(?)??
?
0
)
it follows that the value at time t
1
of
C
due at time t
2
is:
𝐶
𝑣(?
2
)
𝑣(?
1
)
This tells us that in order to find the value at time t
1
of
C
due at time t
2
, we can discount both amounts back
to time 0, and then calculate the difference.
Question:
Calculate the value at time 4 of a payment of 860 at time 10 if
𝑣(10) = 0.76
and
𝑣(4) = 0.91
.
Solution:
The value at time 4 is:
860 ×
𝑣(10)
𝑣(4)
= 860 ×
0.76
0.91
= 718.24

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