professor’s annuity corporation offers a lifetime annuity to retiring professors. for a payment of $82,000 at age 65, the firm will pay the retiring professor $650 a month until his death.

Respuesta :

The APR=12*i=7.805271% or the effective interest rate is

(1+i)^12-1=8.09064%

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

Calculate i=0.00650439, or 0.650439%, by using Newton's technique, fix-point iteration, or the F1=F2 equation as a starting point.

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%

What is an annuity?

A sequence of payments given at regular intervals is known as an annuity. Examples of annuities include pension payments, regular deposits into a savings account, monthly insurance payments, house mortgage payments, and home mortgage payments. By how frequently payment dates occur, annuities can be categorized. The payments (deposits) may be paid every week, every month, every four months, every year, or at any other regular frequency. Mathematical operations referred to as "annuity functions" can be used to compute annuities.

A life annuity is an annuity that offers payments throughout the balance of the owner's lifetime.

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