Joanna has taken an endowment policy that matures in $30$ years. The expected

interest rate per year is $11\mathrm{.}15\%.$ Her annual payment $($at the end of each year$)$ is

P$8000.$ Calculate:

i$.$ The present value of the policy $(4$ marks$)$

ii$.$ The future value of the policy $(4$ marks$)$

c$.$ Find the value of $$10,000$ in $10$ years. The investment earns $8\%$ for four years and

then earns $4\%$ for the remaining six years. $(4$ marks$)$

d$.$ P$1400$ was left in an investment account for $20$ years and it earned $12\mathrm{.}5\%$ per

year compounded half$-$yearly. Calculate the value of the investment after $20$ years.