Account-value path for Type A universal life

Computes the year-by-year account value roll-forward for Type A universal life using the explicit form in Equation (16.8), or Equation (16.9) when \(i^q = i^c\).

Usage

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

Arguments

G

Premium vector \(G_t\).

r

Percent-of-premium expense vector \(r_t\).

e

Fixed expense vector \(e_t\).

qx

Mortality vector \(q_{x+t-1}\).

ic

Credited interest rate vector \(i^c\).

B

Fixed death benefit face amount.

iq

Interest rate vector \(i^q\) used in cost of insurance. Defaults to ic.

AV0

Initial account value. Defaults to 0.

Value

A data frame with columns t, premium, AV.

Examples

qx <- c(.00076, .00081, .00085, .00090, .00095)
r <- c(.75, .10, .10, .10, .10)
e <- c(100, 20, 20, 20, 20)
G <- rep(5000, 5)

AV_path_ul_typeA(G = G, 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