Today is January $12021,$ Jacob will use a single premium to purchase an annuity today. This annuity pays $10,000$ at the end of each year while Jacob is alive. The estimated probability of Jacob surviving for the next $4$ years is stated in following table. The yield rate is assumed to be j$1=2\mathrm{.}87\%$ p$.$a$.$ Calculate premium value. Round your answers to three decimal places.

Year $|$ Probability of surviving from start of year to end of year

$1|0\mathrm{.}78$

$2|0\mathrm{.}61$

$3|0\mathrm{.}43$

$4|0$

a$.$

$18200\mathrm{.}000$

b$.$

$13958\mathrm{.}032$

c$.$

$17198\mathrm{.}632$

d$.$

$17296\mathrm{.}809$