第一章习题答?/p>
1.
设总量函数?/p>
A
(
t
) =
t
2 + 2
t
+ 3
。试计算累积函数
a
(
t
)
和第
n
个时段的利息
In
?/p>
?/p>
:
?/p>
t
= 0
代入?/p>
A
(0) = 3
于是
:
a
(
t
) =
A
(
t
)
A
(0)
=
t
2 + 2
t
+ 3
3
In
=
A
(
n
)
?/p>
A
(
n
?/p>
1)
= (
n
2 + 2
n
+ 3)
?/p>
((
n
?/p>
1)2 + 2(
n
?/p>
1) + 3))
= 2
n
+ 1
2.
对以下两种情况计算从
t
时刻?/p>
n
(
t < n
)
时刻的利?/p>
: (1)
Ir
(0
< r <
n
); (2)
Ir
= 2
r
(0
< r < n
)
.
?/p>
:
(1)
I
=
A
(
n
)
?/p>
A
(
t
)
=
In
+
In
¡
1 +
?/p>
?/p>
?/p>
+
It
+1
=
n
(
n
+ 1)
2
?/p>
t
(
t
+ 1)
2
(2)
I
=
A
(
n
)
?/p>
A
(
t
)
=
Σ
n
k
=
t
+1
Ik
=
Σ
n
k
=
t
+1
Ik
= 2
n
+1
?/p>
2
t
+1
3.
已知累积函数的形式为
:
a
(
t
) =
at
2 +
b
。若
0
时刻投入?/p>
100
元累积到
3
时刻
?/p>
172
元,试计算:
5
时刻投入?/p>
100
元在
10
时刻的终值?/p>
?/p>
1
?/p>