a$)$ What is the PV of receiving $2,000/$year starting in $3$ years going for $17$ years if the discount rate is $11\%?$

b$)$ What is the NPV of a project that costs $$1,500,000$ and generates $140,000/$year forever if the discount rate is $9\%?$

c$)$ A project will provide in $3$ years either $$12,000$ with $30\%$ probability, $$22,000$ with a $20\%$ probability, $$38,000$ with a $40\%$ probability, and $$79,000$ with a $10\%$ probability. Given an $8\%$ discount rate, what is its expected PV$?$