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
=