A University is offering a charitable gift program. A former student who is now $50$ years old is consider the following

offer: The student can invest $$7,700\mathrm{.}00$ today and then will be paid a $8\mathrm{.}00\%$ APR return starting on his $65$ th birthday $($i$.$e

For a $$10,000$ investment, a $9\%$ rate would mean $$900$ per year$).$ The program will pay the cash flow for this investment

while you are still alive. You anticipate living $25\mathrm{.}00$ more years after your $65$th birthday. The former student wants a

return of $6\mathrm{.}00\%$ on his investments, but would like to consider this opportunity.

Using the student's desired return, what is the value of this deferred annuity today on his $50$ th birthday?