Type A universal life account-value path

Computes a year-by-year Type A universal life account-value path. The death benefit is fixed, so the net amount at risk depends on the ending account value and the roll-forward is solved explicitly each period.

Usage

AV_path_ul_typeA(G, r, e, qx, ic, B, iq = ic, AV0 = 0)

Arguments

G

Premium amount by period.

r

Percent-of-premium expense rate by period. Values must lie in [0, 1].

e

Fixed expense by period.

qx

Mortality probability by period.

ic

Credited annual effective interest rate by period. Values must be greater than -1.

B

Face amount by period.

iq

Interest rate used in the cost-of-insurance calculation. Defaults to ic; values must be greater than -1.

AV0

Nonnegative scalar initial account value.

Value

A data frame containing the policy duration, premium, and account value.

Examples

qx <- c(0.00076, 0.00081, 0.00085, 0.00090, 0.00095)
r <- c(0.75, rep(0.10, 4))
e <- c(100, rep(20, 4))

AV_path_ul_typeA(
  G = 5000,
  r = r,
  e = e,
  qx = qx,
  ic = 0.03,
  B = 100000
)
#>   t premium        AV
#> 1 0      NA     0.000
#> 2 1    5000  1109.343
#> 3 2    5000  5680.625
#> 4 3    5000 10389.274
#> 5 4    5000 15239.068
#> 6 5    5000 20234.863