Rates are currently 7% p.a. You wish to purchase a security that pays out $500 each 3 months starting in exactly 2 months time. The security will pay out a total of 30 payments.

What is the fair purchase price of the security?

b. Assume that you purchased the above security. Imagine that exactly 1 year has passed. You now wish to sell the security. However, interest rates have now fallen to 6% p.a. compounded monthly. What is the fair selling price of the security?

Please show step by step calculations and work!