Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 143, 2/9/8
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November 2001 Course 2 Examination, Problem No. 28, also Study Note FM-09-05,
Problem No. 21
Payments are made to an account at a continuous rate of 8k + tk, where 0 ! t ! 10.
1
Interest is credited at a force of interest ! t =
. After 10 years, the account is worth
8+t
20000. Calculate k.
A. 111
B. 116
C. 121
D. 126
E. 131
Solution.
Note that
10
10
! 8 +t dt
a (10 )
eln18
18
ln ( 8 +t ) n
=e
= en
= ln ( 8 + n ) =
.
a (n)
8+n
e
Therefore,
10
10
10
a (10 )
18
20000 = " ( 8k + tk ) !
dt = " k ! ( 8 + t ) !
dt = " 18kdt = 180k.
!
#"#
$
a (t )
8+t
0 Rate of payment
0
0
%
1
Accumulates the
payment from
time t to time 10
This implies that
20, 000
k=
! 111.
180
Answer A.
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