ABC is an investment company that offers a $3-$

year GIC paying interest at j$2=5\%.$ Mr$.$ Smith

is an investor who buys a $$10003-$year GIC

from ABC.

a$)$What is the maturity value of the GIC for

Mr$.$ Smith?

b$)$To back up this liability to Mr$.$ Smith, ABC

purchases a $3-$year accumulation bond with

face value $$1000,$ paying interest at j$2=6\%.$

Assuming no expenses, what profit will

ABC make after $3$ years?

c$)$One year later, Mr$.$ Smith sees that interest

rates have risen and he wants to cash in his

$3-$year GIC $($suppose he can do this with no

penalty$).$ How much will he receive?

d$)$To pay Mr$.$ Smith, ABC must cash in their

$3-$year bond $(2$ years before maturity$).$

Suppose yield rates have risen to j$2=7\%.$

What profit$/$loss does ABC make after $1-$

year?