Question

Table 1: Survival probability Year Probability of surviving from start of year to end of year

Year 1 - 0.75

Year 2 . - 0.58

Year 3 - 0.37

Year 4 - 0.23

Year 5 - 0 e.

Jackson will use $50,000 from the total sale proceed of instruments as a single premium to purchase an annuity today. This annuity pays X at the end of each year while Jackson is alive. The estimated probability of Jackson surviving for the next 5 years is stated in table 1. The yield rate is assumed to be j1 = 3.2% p.a. Calculate X value. Round your answers to three decimal places. Draw a detailed contingent cash flow diagram for instrument D, from the perspective of Jackson

Answer 1

We can use following Present Value of an Annuity formula to calculate the value of annuity payment X at the end of each year.

PV of sale proceed today = PMT* [1-(1+i) ^-n)]/i

Where,

Present value (PV) = $50,000

Annual payment PMT = X

Number of payments n = 5

Annual interest rate or yield rate i =3.2%

Therefore

$50,000 = X * [1- (1+0.032) ^-5]/ (0.032)

Or X = $10,980.150

Therefore annuity payment at the end of each year is $10,980.150.

Now Contingent cash flow table based of annuity payment per year

Survival probability Year	Probability of surviving from start of year to end of year	Annuity payment at the end of each year	Contingent cash flow = (Probability * annuity payment)
0			-$50,000
1	0.75	$10,980.150	$8,235.113
2	0.58	$10,980.150	$6,368.487
3	0.37	$10,980.150	$4,062.656
4	0.23	$10,980.150	$2,525.435
5	0	$10,980.150	$0