You have a bond with a maturity value of $$6000,$ a coupon rate of $5\%,$ and an expiration date $4$ years from now.

a$)$ What is today's present value, assuming a discount rate of $3\%?$

b$)$ The company announces that new sanctions will hit the business and after careful analysis you believe that the company's risk increases $40\%.$ What will be the new present value when taking this into account?

c$)$ Due to ongoing geopolitical uncertainty, the Fed decides to inject more money to the economy and lower interest rates further, by about $35\%.$ Compared to a$),$ and ignoring the info scenario in b$),$ what is the new present value of this bond?

$($for b and c assume that the discount rate is updated proportionally to the percentage changes$)$