Question

For purposes of compensation, an actuary working for a lawyer estimates the annual earnings of a September 11 victim that died at the Twin Towers at age 32. The victim was making $95,000 a year and a stream of payments for that amount would have likely accrued to her annually until retirement at age 65. The actuary knows that this is an ordinary annuity problem. He assumes, as is usual, that the victim's salary would grow in tandem with inflation, which for years has hovered at around 3% annually. What is the future value of this annuity, the minimum basis for a possible settlement with the relatives of the victim, if a fair settlement were indeed on the table?

Answer 1

SOLUTION:

Following information is given:

• Current age is 32
• The retirement age is 65 the year left for retirement
• The years left is 33 years for retirement
• The current value payment received is $ 95,000
• The rate of inflation or interest is 3% annually

We have to calculate the future value of annuity.

Annuity formula is used when regular payments are made or received

The Formula for FVA(future value of annuity is given below

FVAt= PMT{(1+i/m)mt - 1]/i/m)}

Where FVAt = future value of annuity at the end of the year t in this case 33 years

PMT = the annuity payments which occurs m times in a year in this case $95000

I =annual interest rate in this case 3% or 0.03

T= number of years in this case 33 years

M= number of compounding periods in a year in this case 1 times in year amount is deposited

Mt= number of payments and compounding periods in t years

Putting values in the formula we get

FVAt= PMT{(1+i/m)mt - 1]/i/m)}

= $95000 {(1+.03/1)33 - 1]/0.03/1)}

= $95000 {(1+.03)33 - 1]/0.03)}

= $95000 {(1.03)33 - 1]/0.03)}

= $95000 {( 2.652335- 1]/0.03)}

= $95000 {( 1.652335]/0.03)}

= $95000 x 55.07784

= $5232394.92

=$ 5232395(( rounding off to nearest dollar)

The future value of this annuity is $5,232,395

If there fair settlement now than Present value of annuity will be calculated

Then we will calculate the trsent value of annuity

The formula is

P = PMT [(1 - (1 / (1 + r)n)) / r]

Where PMT = $95,000

R = 0.03 0r 3 %

N= 33 years

Putting value in the formual

P = $95,000 [(1 - (1 / (1 + .03)33)) / 0.03]

= $95,000 [(1 - (1 / (1 .03)33)) / 0.03]

= $95,000 [(1 - (1 / (2.652335238)) / 0.03]

= $95,000 [(1 - 0.377026247/ 0.03]

= $95,000 [(0.622973753/ 0.03]

= $95,000 x 20.76579178

=1972750.219

The present value at fair settlement can be now is $1972750.219 or $1,972,750