An employee's compensation includes an annuity with $7$ annual payments that pays $$80,000$ at retirement, with each subsequent payment growing by $4\%.$ The firm$$s policy is to pre$-$fund such annuities one year before retirement. At an interest rate of $6\%,$ how much would the firm need to invest?

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.