Professor's annuity corp. offers a lifetime annuity to retiring professors. for a payment of $90,000 at age 65, the firm will pa

Question

3 years ago

10

Professor's annuity corp. offers a lifetime annuity to retiring professors. for a payment of $90,000 at age 65, the firm will pa

y 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?

Mathematics

1 answer:

vovangra [49] · Answer 1 · 2022-05-14T17:58:15+03:00

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%