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$1=2\mathrm{.}27\%$ p$.$a$.$ Calculate premium value. Round your answers to three decimal places.

Year

Probability of surviving from start of year to end of year

$10\mathrm{.}86$

$20\mathrm{.}69$

$30\mathrm{.}39$

$40$

Question $11$Answer

a$.$

$19400\mathrm{.}000$

b$.$

$18548\mathrm{.}347$

c$.$

$18652\mathrm{.}232$

d$.$

$16246\mathrm{.}165$