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Answer the following time value of money questions assuming the interest rate is $5$ percent.

a$.$ What is the present value of $$1,500$ to be received in four years?

b$.$ What is the present value of $$1,500$ to be received in eight years?

c$.$ What will be the value in seven years of $$12,000$ invested today?

d$.$ How much would you pay for the right to receive $$5,000$ at the end of year $1,$$$4,000$ at the end of year $2,$ and $$8,000$ at the end of year $5?$

e$.$ How long will it take for a $$2,000$ investment to double in value?

f$.$ What will be the value in $20$ years of $$1,800$ invested at the end of each year for the next $20$ years?

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

$\backslash$table$[[$a$.PV,,],[$b$.PV,,],[$c$.$ FV$,,],[$d$.PV,,],[$e$.$ Number of time,,years$],[$f$.$ FV$,,]]$