Question $10$

You are given a perpetuity, with annual payments as follows:

i$.$ Payments of $$2$ at the end of the first year and every three years thereafter

ii$.$ Payments of $$1$ at the end of the second year and every three years thereafter

iii. Payments of $$3$ at the end of the third year and every three years thereafter

The interest rate is $$ convertible semi$-$annually

Calculate the present value of this perpetuity

alpha $=10\%$