Question

At retirement in December, you buy a special type of insurance policy called an immediate term annuity. This policy promises to pay the holder (or the holder’s heirs) $25,000 per year for the next 26 years. Each payment is at the start of the year. (Hence, the first payment will be very shortly after purchase of the policy.) The appropriate discount rate is 5.09% per year, compounded annually. What is the value of this policy to the policy holder? Do not round at intermediate steps in your calculation. Report your answer in dollars. Enter your answer without the $ symbol.

Answer 1

Information provided:                                                                                            

Annual payment= $25,000

Time= 26 years

Discount rate= 5.09%

The question is concerning finding the present value of an annuity due since the question mentions that the annuity is paid from today.  Annuity due refers to annuity that occurs at the beginning of a period.

This can also be solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2^ndBGN 2^ndSET on the Texas BA II Plus calculator.

Enter the below in a financial calculator to calculate the present value of the annuity:

PMT= 25,000

N= 26

I/Y= 5.09

Press the CPT and PV to compute the present value.

The value obtained is 374,192.13.

Therefore, the value of this policy to the policy holder is $374,192.13.