Today is January 1, 2022. Roy will use a single premium to purchase an annuity today. This annuity pays $10,000 at the end of each year while Roy is alive. The estimated probability of Roy surviving for the next 4 years is stated in following table. The yield rate is assumed to be j₁ = 6.5% p.a. Calculate the premium value. Round your answer to three decimal places.

Year	Probability of surviving from start of year to end of year
1	0.96
2	0.65
3	0.5
4	0

a.

$17098.528

b.

$18884.115

c.

$21100.000

d.

$18603.011

2.

Today is 1 July, 2019. Siobhn has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Siobhn purchased all instruments on 1 July 2014 to create this portfolio, which is composed of 34 units of instrument A and 29 units of instrument B.

• Instrument A is a zero-coupon bond with a face value of $100. This bond matures at par. Its maturity date is 1 January 2029.
• Instrument B is a Treasury bond with a coupon rate of j₂=3.89% p.a. and a face value of $100. This bond matures at par. Its maturity date is 1 January 2022.

Calculate the current duration of Siobhns portfolio using a yield to maturity of j₂=4.97% p.a. Express your answer in terms of years and round your answer to two decimal places.

a.

5.29 years

b.

6.50 years

c.

5.46 years

d.

6.92 years