Titan Corporation provides a retirement plan for itd employees. One of its emplo

Question

Titan Corporation provides a retirement plan for itd employees. One of its employees has vested benefits under the plan which will pay her $30,000 annually for life starting with the first $30,000 payment on the day she retires at the age of 65. The employee has just turned 45 years old. Titan consulted standard mortality tables to come up with a life expectancy of 80 for this employee. (Assume the last payment is on the employee's 79Th dirthday.) The interest rate under the plan is 9%. Draw a timeline from age 45 to age 80 showing the anticipated payment schedule. What will br the present value of the pension obligation at the time of the employee's retirement (age 65)? What is the present value of the pension obligation at the current time(age 45)?

Explanation / Answer

Formula for Annuity fund :

P= r(PV)/ 1-(1+r)-n

Where P = Annuity payment received =$30,000/year

n=No of period =15 years

PV = Fund value of Annuity to be invested

R=rate of interest =9% pa

30,000= 0.09*PV/[1-(1.09)-15 =0.09PV/0.725

Or PV = 30,000*0.725/0.09=241,666.66

b.

So present value of pension obligation at the age of 65 is $241,666.66

c.

Present value of $ 241,666.66 now , or 20 years back is =241,666.66/(1.09)20

=241,666.66/5.604 =$ 43,123.95

So current value of the obligation =$ 43,123.95

1. Timeline Current Investment $43123.95 At age 65 ……………. Upto age 80/15 installments ……….. At age 45 $30,000 $30,000 $30,000 $30,000 $30,000 $30,000

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