Question

Today is January 1 2020, Jackson will use a single premium to purchase an annuity today. This annuity pays 10,000 at the end of each year while Jackson is alive. The estimated probability of Jackson surviving for the next 4 years is stated in following table. The yield rate is assumed to be j₁ = 3.87% p.a. Calculate premium value. Round your answers to three decimal places.

Year///////// Probability of surviving from ////////////Star of year to end of year

1 ////////////////////////0.84/////////////////////////////////////////////

2//////////////////////// 0.51////////////////////////////////////////////

3 /////////////////////////0.47/////////////////////////////////////////////

4 //////////////////////////0

Select one:

a. 17008.069

b. 13854.457

c. 16869.069

d. 18200.000

Answer 1

Here, Jackson pays annuity 10000 at the end of each year i.e Present value of annuity

The estimated probability of Jackson for surviving next 4 years is given as-

For year 1= 0.84, For Year 2 = 0.51, For Year 3 = 0.47 and finally For Year 4 = 0.

Therefore, Premium Value are computed as follows-

Year Probability of surviving Premium value

  ​​ {Present value of Annuity * Probability}

1 0.84 10000*0.84 = 8400

2 0.51 10000*0.51

= 5100

3 0.47 10000*0.47

= 4700

4 0 10000*0 = 0

Hence,

8400 + 5100 + 4700 + 0 = 18200 That is the premium value.

So the correct option is d. 18200.