$2.$ Problem $5\mathrm{.}02($Present Value$)$

What is the present value of a security that will pay $$28,000$ in $20$ years if securities of equal risk pay $8\%$ annually? Do not round intermediate calculations. Round your answer to the nearest cent.

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$3.$ Problem $5\mathrm{.}03($Finding the Required Interest Rate$)$

Your parents will retire in $27$ years. They currently have $$360,000$ saved, and they think they will need $$2,050,000$ at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

$\%$

$4.$ Problem $5\mathrm{.}04($Time for a Lump Sum to Double$)$

If you deposit money today in an account that pays $13\%$ annual interest, how long will it take to double your money? Round your answer to two decimal places.

years