Head & Shoulders shampoo insured a spokesman football player$$s long hair for $$1$ million with Lloyd's of London. The insurance payout would be triggered if he lost at least $60\%$ of his hair during an on$-$field event. The insurance company placed the odds of a payout at $1\%$ in year $6\mathrm{.}00.$ Determine how much Head and Shoulders had to pay in a lump sum amount for the insurance policy, if Lloyd$$s of London wanted a rate of return of $20\%$ per year, compounded semi$-$annually.

If Lloyd's of London wanted a rate of return of $20\%,$ Head and Shoulders had to pay $

in a lump sum amount for the insurance policy.