A financial institution offers a "double$-$your$-$money" savings account in which you will have $$2$ in $7$ years for every dollar you invest today. What annual interest rate does this account offer?

Please specify your answer in decimal terms and round your answer to the nearest thousandth $($e$.$g$.,$ enter $12\mathrm{.}3$ percent as $0\mathrm{.}123).$

Please round your answer to the nearest hundredth.

Please round your answer to the nearest hundredth.

Please round your answer to the nearest hundredth.

Equivalent problem structure $($in neutral time$-$value$-$of$-$money terms$)$: What is the present value of a series of payments received each year for $7$ years, starting with $$80,000$ paid one year from now and the payment growing in each subsequent year by $4\%?$ Assume a discount rate of $6\%.$

Please round your answer to the nearest hundredth.

Equivalently: What amount would you have to invest today at an interest rate of $10\%$ to generate an annual payment forever, starting with $$1,400$ and the payment growing in each subsequent year by $8\%?$

Please round your answer to the nearest hundredth.