Today is January $12021,$ 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 j$1=4\mathrm{.}75\%$ p$.$a$.$ Calculate premium value. Round your answers to three decimal places.

Year

Probability of surviving from start of year to end of year

$10\mathrm{.}71$

$20\mathrm{.}51$

$30\mathrm{.}24$

$40$

Question $11$ Answer

a$.$

$13305\mathrm{.}916$

b$.$

$10834\mathrm{.}190$

c$.$

$13514\mathrm{.}090$

d$.$

$14600\mathrm{.}000$