Answer the following time value of money questions assuming the interest rate is $4$ percent.

a$.$ What is the present value of $$500$ to be received in four years?

b$.$ What is the present value of $$500$ to be received in eight years?

c$.$ What will be the value in seven years of $$11,000$ invested today?

d$.$ How much would you pay for the right to receive $$4,000$ at the end of year $1,$$$3,000$ at the end of

year $2,$ and $$7,000$ at the end of year $5?$

e$.$ How long will it take for a $$1,000$ investment to double in value?

f$.$ What will be the value in $20$ years of $$800$ invested at the end of each year for the next $20$ years?

Note: Round your answers to $2$ decimal places.