Suppose that the annual percentage rate (compounded annually) is 10%. Calculate the present value of the following perpetuities:

a perpetuity that pays $500 every year with the first payment occurring in 2 years from now;

(b) a perpetuity that pays $500 every year with the first payment occurring in 3 years from now;

(c) a perpetuity that pays $500 every six months with the first payment occurring in 4 years from now;

(d) a perpetuity payable annually with the first payment of $100 now and each additional payment growing at 2% annually.