Professor's annuity corp. offers a lifetime annuity to retiring professors. for a payment of $90,000 at age 65, the firm will pay the retiring professor $850 a month until death. a. if the professor's remaining life expectancy is 15 years, what is the monthly interest rate on this annuity?

This can be solved by equating the future value of the payment F1, and the future value of the annuity F2, after n=12*15=180 months.
i is the monthly interest.
P=payment of 90000
A=monthly amount of 850

F1=P(1+i)^n=90000(1+i)^180
F2=A*((1+i)^n-1)/i=850((1+i)^180-1)/i

equate F1=F2 and solve for i (only unknown) by trial and error, fix-point iteration or Newton's method to get i=0.00650439,or 0.650439%
The monthly interest rate is 0.650439%.

Therefore the APR=12*i=7.805271%, or the effective interest rate is
(1+i)^12-1=8.09064%