4A Interest Theory

( timothy.regan@zurich.com )
Thu, 16 Jul 1998 15:56:21 -0500

I'm afraid I have to disagree with the answers I've seen for Carolyn's
question. The one area that they run into problems is that they seem t=
o be
treating the force of interest as a yearly interest rate instead of the=

total interest rate for the period. The purpose of having the function=
is
to give the cumulative rate for the total period. Here is what I came =
up
with, broken into parts (i) and (ii):

i.) The current value of 1000 @ t=3D2 brought forward to t=3D4 is
1000(1+(.05)(2)) =3D 1100

The current value of 400 @ t=3D7 brought back to t=3D4 is simply
400exp**[ - { (.2 / (1+.2t))dt ] t=3D4 to 7 =3D 377.64
( I'm using { as the integral symbol )

Therefore, the current value at t=3D4 is 1477.64

ii.) Bringing the value of X @ t=3D10 back to time t=3D0 is
X / [(1+(.05)(4))(exp**[ { (.2 / (1+.2t))dt ] t=3D4 to 10]

Because (i) and (ii) are equal, the resulting equation is

1477.64 =3D X / [(1+(.05)(4))(exp**[ { (.2 / (1+.2t))dt ] t=3D4 t=
o 10]
X =3D [1477.64] [(1+(.05)(4))(exp**[ { (.2 / (1+.2t))=
dt ]
t=3D4 to 10]
X =3D 1963.90

=