R/calcfuncsch8.R
In ChrisGroendyke/AutoSULT: Automatic Mortality Table Problem Generation
Defines functions
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# R Code File Containing Problem / Solution Functions #
############################################################
# Chapter 8
#### Define calculation function types
problistch8 <- list()
problistch8[[1]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{00}}$
{
tpx00 <- round(SSD[age, 10] * SSD[age+10, 10] + SSD[age, 11] * SSD[age+10, 13], 5)
s.prob <- paste0(s.tpxij(age, 20, 0, 0))
s.ans <- paste0(s.tpxij(age, 20, 0, 0),"=", s.plus(s.times(s.tpxij(age, 10, 0, 0), s.tpxij(age+10, 10, 0, 0)), s.times(s.tpxij(age, 10, 0, 1), s.tpxij(age+10, 10, 1, 0))), "=", s.plus(s.times(SSD[age, 10], SSD[age+10, 10]), s.times(SSD[age, 11], SSD[age+10, 13])), "=", fbox(tpx00, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx00))
}
problistch8[[2]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{01}}$
{
tpx01 <- round(SSD[age, 10] * SSD[age+10, 11] + SSD[age, 11] * SSD[age+10, 12], 5)
s.prob <- paste0(s.tpxij(age, 20, 0, 1))
s.ans <- paste0(s.tpxij(age, 20, 0, 1),"=", s.plus(s.times(s.tpxij(age, 10, 0, 0), s.tpxij(age+10, 10, 0, 1)), s.times(s.tpxij(age, 10, 0, 1), s.tpxij(age+10, 10, 1, 1))), "=", s.plus(s.times(SSD[age, 10], SSD[age+10, 11]), s.times(SSD[age, 11], SSD[age+10, 12])), "=", fbox(tpx01, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx01))
}
problistch8[[3]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{02}}$
{
tpx00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx02 <- 1 - tpx00$num.ans - tpx01$num.ans
s.prob <- paste0(s.tpxij(age, 20, 0, 2))
s.ans <- paste0(s.tpxij(age, 20, 0, 2),"=", s.minus(1, s.minus(s.tpxij(age, 20, 0, 0), s.tpxij(age, 20, 0, 1))), "=", s.minus(1, s.minus(tpx00$num.ans, tpx01$num.ans)), "=", fbox(tpx02, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", tpx00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", tpx01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx02))
}
problistch8[[4]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{10}}$
{
tpx10 <- round(SSD[age, 13] * SSD[age+10, 10] + SSD[age, 12] * SSD[age+10, 13], 5)
s.prob <- paste0(s.tpxij(age, 20, 1, 0))
s.ans <- paste0(s.tpxij(age, 20, 1, 0),"=", s.plus(s.times(s.tpxij(age, 10, 1, 0), s.tpxij(age+10, 10, 0, 0)), s.times(s.tpxij(age, 10, 1, 1), s.tpxij(age+10, 10, 1, 0))), "=", s.plus(s.times(SSD[age, 13], SSD[age+10, 10]), s.times(SSD[age, 12], SSD[age+10, 13])), "=", fbox(tpx10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx10))
}
problistch8[[5]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{11}}$
{
tpx11 <- round(SSD[age, 13] * SSD[age+10, 11] + SSD[age, 12] * SSD[age+10, 12], 5)
s.prob <- paste0(s.tpxij(age, 20, 1, 1))
s.ans <- paste0(s.tpxij(age, 20, 1, 1),"=", s.plus(s.times(s.tpxij(age, 10, 1, 0), s.tpxij(age+10, 10, 0, 1)), s.times(s.tpxij(age, 10, 1, 1), s.tpxij(age+10, 10, 1, 1))), "=", s.plus(s.times(SSD[age, 13], SSD[age+10, 11]), s.times(SSD[age, 12], SSD[age+10, 12])), "=", fbox(tpx11, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx11))
}
problistch8[[6]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{12}}$
{
tpx10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx12 <- 1 - tpx10$num.ans - tpx11$num.ans
s.prob <- paste0(s.tpxij(age, 20, 1, 2))
s.ans <- paste0(s.tpxij(age, 20, 1, 2),"=", s.minus(1, s.minus(s.tpxij(age, 20, 1, 0), s.tpxij(age, 20, 1, 1))), "=", s.minus(1, s.minus(tpx10$num.ans, tpx11$num.ans)), "=", fbox(tpx12, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", tpx10$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", tpx11$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx12))
}
problistch8[[7]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{00}$
{
termann10 <- round(SSD[age, 2] - (1.05^(-10))*SSD[age, 10]*SSD[age+10, 2] - (1.05^(-10))*SSD[age, 11]*SSD[age+10, 5], 5)
s.prob <- paste0(s.conttermannij(age, 0, 0, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 0)), s.contWLannij(age+10, 0, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 1)), s.contWLannij(age+10, 1, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 10]), SSD[age+10, 2]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 11]), SSD[age+10, 5]))
s.ans <- paste0(s.conttermannij(age, 0, 0, 10),"=", s.minus(s.contWLannij(age, 0, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 2], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[8]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{01}$
{
termann10 <- round(SSD[age, 3] - (1.05^(-10))*SSD[age, 10]*SSD[age+10, 3] - (1.05^(-10))*SSD[age, 11]*SSD[age+10, 4], 5)
s.prob <- paste0(s.conttermannij(age, 0, 1, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 0)), s.contWLannij(age+10, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 1)), s.contWLannij(age+10, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 10]), SSD[age+10, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 11]), SSD[age+10, 4]))
s.ans <- paste0(s.conttermannij(age, 0, 1, 10),"=", s.minus(s.contWLannij(age, 0, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 3], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[9]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{10}$
{
termann10 <- round(SSD[age, 5] - (1.05^(-10))*SSD[age, 12]*SSD[age+10, 5] - (1.05^(-10))*SSD[age, 13]*SSD[age+10, 2], 5)
s.prob <- paste0(s.conttermannij(age, 1, 0, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 1)), s.contWLannij(age+10, 1, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 0)), s.contWLannij(age+10, 0, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 12]), SSD[age+10, 5]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 13]), SSD[age+10, 2]))
s.ans <- paste0(s.conttermannij(age, 1, 0, 10),"=", s.minus(s.contWLannij(age, 1, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 5], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[10]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{11}$
{
termann10 <- round(SSD[age, 4] - (1.05^(-10))*SSD[age, 13]*SSD[age+10, 3] - (1.05^(-10))*SSD[age, 12]*SSD[age+10, 4], 5)
s.prob <- paste0(s.conttermannij(age, 1, 1, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 0)), s.contWLannij(age+10, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 1)), s.contWLannij(age+10, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 13]), SSD[age+10, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 12]), SSD[age+10, 4]))
s.ans <- paste0(s.conttermannij(age, 1, 1, 10),"=", s.minus(s.contWLannij(age, 1, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 4], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[11]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{00}$
{
twentyp00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 2] - (1.05^(-20))*twentyp00$num.ans*SSD[age+20, 2] - (1.05^(-20))*twentyp01$num.ans*SSD[age+20, 5], 5)
s.prob <- paste0(s.conttermannij(age, 0, 0, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 0)), s.contWLannij(age+20, 0, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 1)), s.contWLannij(age+20, 1, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp00$num.ans), SSD[age+20, 2]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp01$num.ans), SSD[age+20, 5]))
s.ans <- paste0(s.conttermannij(age, 0, 0, 20),"=", s.minus(s.contWLannij(age, 0, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 2], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[12]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{01}$
{
twentyp00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 3] - (1.05^(-20))*twentyp00$num.ans*SSD[age+20, 3] - (1.05^(-20))*twentyp01$num.ans*SSD[age+20, 4], 5)
s.prob <- paste0(s.conttermannij(age, 0, 1, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 0)), s.contWLannij(age+20, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 1)), s.contWLannij(age+20, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp00$num.ans), SSD[age+20, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp01$num.ans), SSD[age+20, 4]))
s.ans <- paste0(s.conttermannij(age, 0, 1, 20),"=", s.minus(s.contWLannij(age, 0, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 3], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[13]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{10}$
{
twentyp11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 5] - (1.05^(-20))*twentyp11$num.ans*SSD[age+20, 5] - (1.05^(-20))*twentyp10$num.ans*SSD[age+20, 2], 5)
s.prob <- paste0(s.conttermannij(age, 1, 0, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 1)), s.contWLannij(age+20, 1, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 0)), s.contWLannij(age+20, 0, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp11$num.ans), SSD[age+20, 5]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp10$num.ans), SSD[age+20, 2]))
s.ans <- paste0(s.conttermannij(age, 1, 0, 20),"=", s.minus(s.contWLannij(age, 1, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 5], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp11$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp10$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[14]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{11}$
{
twentyp11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 4] - (1.05^(-20))*twentyp10$num.ans*SSD[age+20, 3] - (1.05^(-20))*twentyp11$num.ans*SSD[age+20, 4], 5)
s.prob <- paste0(s.conttermannij(age, 1, 1, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 0)), s.contWLannij(age+20, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 1)), s.contWLannij(age+20, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp10$num.ans), SSD[age+20, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp11$num.ans), SSD[age+20, 4]))
s.ans <- paste0(s.conttermannij(age, 1, 1, 20),"=", s.minus(s.contWLannij(age, 1, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 4], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp11$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp10$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[15]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{10}}^{02}$
{
termins10 <- round(SSD[age, 7] - (1.05^(-10))*SSD[age, 10]*SSD[age+10, 7] - (1.05^(-10))*SSD[age, 11]*SSD[age+10, 9], 5)
s.prob <- paste0(s.conttermij(age, 0, 2, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 0)), s.contWLij(age+10, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 1)), s.contWLij(age+10, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 10]), SSD[age+10, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 11]), SSD[age+10, 9]))
s.ans <- paste0(s.conttermij(age, 0, 2, 10),"=", s.minus(s.contWLij(age, 0, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 7], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins10))
}
problistch8[[16]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{10}}^{12}$
{
termins10 <- round(SSD[age, 9] - (1.05^(-10))*SSD[age, 13]*SSD[age+10, 7] - (1.05^(-10))*SSD[age, 12]*SSD[age+10, 9], 5)
s.prob <- paste0(s.conttermij(age, 1, 2, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 0)), s.contWLij(age+10, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 1)), s.contWLij(age+10, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 13]), SSD[age+10, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 12]), SSD[age+10, 9]))
s.ans <- paste0(s.conttermij(age, 1, 2, 10),"=", s.minus(s.contWLij(age, 1, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 9], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins10))
}
problistch8[[17]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{20}}^{02}$
{
twentyp00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
termins20 <- round(SSD[age, 7] - (1.05^(-20))*twentyp00$num.ans*SSD[age+20, 7] - (1.05^(-20))*twentyp01$num.ans*SSD[age+20, 9], 5)
s.prob <- paste0(s.conttermij(age, 0, 2, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 0)), s.contWLij(age+20, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 1)), s.contWLij(age+20, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp00$num.ans), SSD[age+20, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp01$num.ans), SSD[age+20, 9]))
s.ans <- paste0(s.conttermij(age, 0, 2, 20),"=", s.minus(s.contWLij(age, 0, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 7], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins20))
}
problistch8[[18]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{20}}^{12}$
{
twentyp11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
termins20 <- round(SSD[age, 9] - (1.05^(-20))*twentyp10$num.ans*SSD[age+20, 7] - (1.05^(-20))*twentyp11$num.ans*SSD[age+20, 9], 5)
s.prob <- paste0(s.conttermij(age, 1, 2, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 0)), s.contWLij(age+20, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 1)), s.contWLij(age+20, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp10$num.ans), SSD[age+20, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp11$num.ans), SSD[age+20, 9]))
s.ans <- paste0(s.conttermij(age, 1, 2, 20),"=", s.minus(s.contWLij(age, 1, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 9], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp11$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp10$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins20))
}
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Defines functions ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ]
############################################################
# R Code File Containing Problem / Solution Functions #
############################################################
# Chapter 8
#### Define calculation function types
problistch8 <- list()
problistch8[[1]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{00}}$
{
tpx00 <- round(SSD[age, 10] * SSD[age+10, 10] + SSD[age, 11] * SSD[age+10, 13], 5)
s.prob <- paste0(s.tpxij(age, 20, 0, 0))
s.ans <- paste0(s.tpxij(age, 20, 0, 0),"=", s.plus(s.times(s.tpxij(age, 10, 0, 0), s.tpxij(age+10, 10, 0, 0)), s.times(s.tpxij(age, 10, 0, 1), s.tpxij(age+10, 10, 1, 0))), "=", s.plus(s.times(SSD[age, 10], SSD[age+10, 10]), s.times(SSD[age, 11], SSD[age+10, 13])), "=", fbox(tpx00, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx00))
}
problistch8[[2]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{01}}$
{
tpx01 <- round(SSD[age, 10] * SSD[age+10, 11] + SSD[age, 11] * SSD[age+10, 12], 5)
s.prob <- paste0(s.tpxij(age, 20, 0, 1))
s.ans <- paste0(s.tpxij(age, 20, 0, 1),"=", s.plus(s.times(s.tpxij(age, 10, 0, 0), s.tpxij(age+10, 10, 0, 1)), s.times(s.tpxij(age, 10, 0, 1), s.tpxij(age+10, 10, 1, 1))), "=", s.plus(s.times(SSD[age, 10], SSD[age+10, 11]), s.times(SSD[age, 11], SSD[age+10, 12])), "=", fbox(tpx01, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx01))
}
problistch8[[3]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{02}}$
{
tpx00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx02 <- 1 - tpx00$num.ans - tpx01$num.ans
s.prob <- paste0(s.tpxij(age, 20, 0, 2))
s.ans <- paste0(s.tpxij(age, 20, 0, 2),"=", s.minus(1, s.minus(s.tpxij(age, 20, 0, 0), s.tpxij(age, 20, 0, 1))), "=", s.minus(1, s.minus(tpx00$num.ans, tpx01$num.ans)), "=", fbox(tpx02, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", tpx00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", tpx01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx02))
}
problistch8[[4]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{10}}$
{
tpx10 <- round(SSD[age, 13] * SSD[age+10, 10] + SSD[age, 12] * SSD[age+10, 13], 5)
s.prob <- paste0(s.tpxij(age, 20, 1, 0))
s.ans <- paste0(s.tpxij(age, 20, 1, 0),"=", s.plus(s.times(s.tpxij(age, 10, 1, 0), s.tpxij(age+10, 10, 0, 0)), s.times(s.tpxij(age, 10, 1, 1), s.tpxij(age+10, 10, 1, 0))), "=", s.plus(s.times(SSD[age, 13], SSD[age+10, 10]), s.times(SSD[age, 12], SSD[age+10, 13])), "=", fbox(tpx10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx10))
}
problistch8[[5]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{11}}$
{
tpx11 <- round(SSD[age, 13] * SSD[age+10, 11] + SSD[age, 12] * SSD[age+10, 12], 5)
s.prob <- paste0(s.tpxij(age, 20, 1, 1))
s.ans <- paste0(s.tpxij(age, 20, 1, 1),"=", s.plus(s.times(s.tpxij(age, 10, 1, 0), s.tpxij(age+10, 10, 0, 1)), s.times(s.tpxij(age, 10, 1, 1), s.tpxij(age+10, 10, 1, 1))), "=", s.plus(s.times(SSD[age, 13], SSD[age+10, 11]), s.times(SSD[age, 12], SSD[age+10, 12])), "=", fbox(tpx11, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx11))
}
problistch8[[6]] <- function(SSD, age, ansbox = TRUE) # ${_{20}p_x^{12}}$
{
tpx10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
tpx12 <- 1 - tpx10$num.ans - tpx11$num.ans
s.prob <- paste0(s.tpxij(age, 20, 1, 2))
s.ans <- paste0(s.tpxij(age, 20, 1, 2),"=", s.minus(1, s.minus(s.tpxij(age, 20, 1, 0), s.tpxij(age, 20, 1, 1))), "=", s.minus(1, s.minus(tpx10$num.ans, tpx11$num.ans)), "=", fbox(tpx12, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", tpx10$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", tpx11$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=tpx12))
}
problistch8[[7]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{00}$
{
termann10 <- round(SSD[age, 2] - (1.05^(-10))*SSD[age, 10]*SSD[age+10, 2] - (1.05^(-10))*SSD[age, 11]*SSD[age+10, 5], 5)
s.prob <- paste0(s.conttermannij(age, 0, 0, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 0)), s.contWLannij(age+10, 0, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 1)), s.contWLannij(age+10, 1, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 10]), SSD[age+10, 2]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 11]), SSD[age+10, 5]))
s.ans <- paste0(s.conttermannij(age, 0, 0, 10),"=", s.minus(s.contWLannij(age, 0, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 2], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[8]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{01}$
{
termann10 <- round(SSD[age, 3] - (1.05^(-10))*SSD[age, 10]*SSD[age+10, 3] - (1.05^(-10))*SSD[age, 11]*SSD[age+10, 4], 5)
s.prob <- paste0(s.conttermannij(age, 0, 1, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 0)), s.contWLannij(age+10, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 1)), s.contWLannij(age+10, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 10]), SSD[age+10, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 11]), SSD[age+10, 4]))
s.ans <- paste0(s.conttermannij(age, 0, 1, 10),"=", s.minus(s.contWLannij(age, 0, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 3], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[9]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{10}$
{
termann10 <- round(SSD[age, 5] - (1.05^(-10))*SSD[age, 12]*SSD[age+10, 5] - (1.05^(-10))*SSD[age, 13]*SSD[age+10, 2], 5)
s.prob <- paste0(s.conttermannij(age, 1, 0, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 1)), s.contWLannij(age+10, 1, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 0)), s.contWLannij(age+10, 0, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 12]), SSD[age+10, 5]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 13]), SSD[age+10, 2]))
s.ans <- paste0(s.conttermannij(age, 1, 0, 10),"=", s.minus(s.contWLannij(age, 1, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 5], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[10]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{10}}^{11}$
{
termann10 <- round(SSD[age, 4] - (1.05^(-10))*SSD[age, 13]*SSD[age+10, 3] - (1.05^(-10))*SSD[age, 12]*SSD[age+10, 4], 5)
s.prob <- paste0(s.conttermannij(age, 1, 1, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 0)), s.contWLannij(age+10, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 1)), s.contWLannij(age+10, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 13]), SSD[age+10, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 12]), SSD[age+10, 4]))
s.ans <- paste0(s.conttermannij(age, 1, 1, 10),"=", s.minus(s.contWLannij(age, 1, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 4], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann10))
}
problistch8[[11]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{00}$
{
twentyp00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 2] - (1.05^(-20))*twentyp00$num.ans*SSD[age+20, 2] - (1.05^(-20))*twentyp01$num.ans*SSD[age+20, 5], 5)
s.prob <- paste0(s.conttermannij(age, 0, 0, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 0)), s.contWLannij(age+20, 0, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 1)), s.contWLannij(age+20, 1, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp00$num.ans), SSD[age+20, 2]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp01$num.ans), SSD[age+20, 5]))
s.ans <- paste0(s.conttermannij(age, 0, 0, 20),"=", s.minus(s.contWLannij(age, 0, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 2], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[12]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{01}$
{
twentyp00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 3] - (1.05^(-20))*twentyp00$num.ans*SSD[age+20, 3] - (1.05^(-20))*twentyp01$num.ans*SSD[age+20, 4], 5)
s.prob <- paste0(s.conttermannij(age, 0, 1, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 0)), s.contWLannij(age+20, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 1)), s.contWLannij(age+20, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp00$num.ans), SSD[age+20, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp01$num.ans), SSD[age+20, 4]))
s.ans <- paste0(s.conttermannij(age, 0, 1, 20),"=", s.minus(s.contWLannij(age, 0, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 3], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[13]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{10}$
{
twentyp11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 5] - (1.05^(-20))*twentyp11$num.ans*SSD[age+20, 5] - (1.05^(-20))*twentyp10$num.ans*SSD[age+20, 2], 5)
s.prob <- paste0(s.conttermannij(age, 1, 0, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 1)), s.contWLannij(age+20, 1, 0)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 0)), s.contWLannij(age+20, 0, 0)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp11$num.ans), SSD[age+20, 5]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp10$num.ans), SSD[age+20, 2]))
s.ans <- paste0(s.conttermannij(age, 1, 0, 20),"=", s.minus(s.contWLannij(age, 1, 0), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 5], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp11$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp10$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[14]] <- function(SSD, age, ansbox = TRUE) # $\\ax*{x:\\angl{20}}^{11}$
{
twentyp11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
termann20 <- round(SSD[age, 4] - (1.05^(-20))*twentyp10$num.ans*SSD[age+20, 3] - (1.05^(-20))*twentyp11$num.ans*SSD[age+20, 4], 5)
s.prob <- paste0(s.conttermannij(age, 1, 1, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 0)), s.contWLannij(age+20, 0, 1)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 1)), s.contWLannij(age+20, 1, 1)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp10$num.ans), SSD[age+20, 3]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp11$num.ans), SSD[age+20, 4]))
s.ans <- paste0(s.conttermannij(age, 1, 1, 20),"=", s.minus(s.contWLannij(age, 1, 1), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 4], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termann20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp11$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp10$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termann20))
}
problistch8[[15]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{10}}^{02}$
{
termins10 <- round(SSD[age, 7] - (1.05^(-10))*SSD[age, 10]*SSD[age+10, 7] - (1.05^(-10))*SSD[age, 11]*SSD[age+10, 9], 5)
s.prob <- paste0(s.conttermij(age, 0, 2, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 0)), s.contWLij(age+10, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 0, 1)), s.contWLij(age+10, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 10]), SSD[age+10, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 11]), SSD[age+10, 9]))
s.ans <- paste0(s.conttermij(age, 0, 2, 10),"=", s.minus(s.contWLij(age, 0, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 7], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins10))
}
problistch8[[16]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{10}}^{12}$
{
termins10 <- round(SSD[age, 9] - (1.05^(-10))*SSD[age, 13]*SSD[age+10, 7] - (1.05^(-10))*SSD[age, 12]*SSD[age+10, 9], 5)
s.prob <- paste0(s.conttermij(age, 1, 2, 10))
s.ans.1 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 0)), s.contWLij(age+10, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{10}", s.tpxij(age, 10, 1, 1)), s.contWLij(age+10, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 13]), SSD[age+10, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-10)), 5), SSD[age, 12]), SSD[age+10, 9]))
s.ans <- paste0(s.conttermij(age, 1, 2, 10),"=", s.minus(s.contWLij(age, 1, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 9], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins10, ansbox))
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins10))
}
problistch8[[17]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{20}}^{02}$
{
twentyp00 <- do.call(problistch8[[1]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp01 <- do.call(problistch8[[2]], list(SSD = SSD, age = age, ansbox = FALSE))
termins20 <- round(SSD[age, 7] - (1.05^(-20))*twentyp00$num.ans*SSD[age+20, 7] - (1.05^(-20))*twentyp01$num.ans*SSD[age+20, 9], 5)
s.prob <- paste0(s.conttermij(age, 0, 2, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 0)), s.contWLij(age+20, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 0, 1)), s.contWLij(age+20, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp00$num.ans), SSD[age+20, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp01$num.ans), SSD[age+20, 9]))
s.ans <- paste0(s.conttermij(age, 0, 2, 20),"=", s.minus(s.contWLij(age, 0, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 7], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp00$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp01$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins20))
}
problistch8[[18]] <- function(SSD, age, ansbox = TRUE) # $\\Ax*{x:\\angl{20}}^{12}$
{
twentyp11 <- do.call(problistch8[[5]], list(SSD = SSD, age = age, ansbox = FALSE))
twentyp10 <- do.call(problistch8[[4]], list(SSD = SSD, age = age, ansbox = FALSE))
termins20 <- round(SSD[age, 9] - (1.05^(-20))*twentyp10$num.ans*SSD[age+20, 7] - (1.05^(-20))*twentyp11$num.ans*SSD[age+20, 9], 5)
s.prob <- paste0(s.conttermij(age, 1, 2, 20))
s.ans.1 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 0)), s.contWLij(age+20, 0, 2)))
s.ans.2 <- paste0(s.times(s.times("v^{20}", s.tpxij(age, 20, 1, 1)), s.contWLij(age+20, 1, 2)))
s.num.ans.1 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp10$num.ans), SSD[age+20, 7]))
s.num.ans.2 <- paste0(s.times(s.times(round((1.05^(-20)), 5), twentyp11$num.ans), SSD[age+20, 9]))
s.ans <- paste0(s.conttermij(age, 1, 2, 20),"=", s.minus(s.contWLij(age, 1, 2), s.minus(s.ans.1, s.ans.2)), "$ \n\\hspace*{0.5in}$\\displaystyle =", s.minus(SSD[age, 9], s.minus(s.num.ans.1, s.num.ans.2)), "=", fbox(termins20, ansbox), ", \\text{ where }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp11$s.ans, ", \\text{ and }$ \n\\hspace*{0.2in}$\\displaystyle", twentyp10$s.ans)
return(list(s.prob=s.prob, s.ans=s.ans, num.ans=termins20))
}
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