Delayed Annuity $($SDT$)$

Christina is planning on buying an insurance policy that will pay for $$142,250$ a year for $25-$years, with the first payment occurring in $15$ years, if she is still alive, otherwise the policy will payout a lump sum to her heirs at the end of year $14.$ The rate of return on the policy is$7\mathrm{.}5$ percent?

What is the value of the lump payout?

If Christina purchases the policy, what is the maximum she is willing to pay?