Calculate the present value of the following single payments:

a$.$ $$10,000$ received five years in the future given a discount of $4\%$

b$.$ $$10,000$ received $10$ years in the future given a discount rate of $4\%$

c$.$ $$10,000$ received five years in the future given a discount rate of $8\%.$ How much different is the value compared to part $($a$)?$

d$.$ $$10,000$ received $10$ years in the future given a discount rate of $8\%.$ How much different is the value compared to part $($c$)?$