To determine the monthly payments for each option, we will use the present value of an annuity formula:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present value (cash value of the policy) = $250,000
PMT = Monthly payment
r = Monthly interest rate = Annual interest rate / 12 = 5% / 12 = 0.4167%
n = Number of months
Option 1: 10 years of monthly payments
n = 10 years * 12 months/year = 120 months
PV = PMT * (1 - (1 + r)^(-n)) / r
$250,000 = PMT * (1 - (1 + 0.04167%)^(-120)) / 0.04167%
Solving for PMT:
PMT = $250,000 * (0.04167%) / (1 - (1 + 0.04167%)^(-120))
PMT ≈ $2,312.62
Option 1 will provide monthly payments of approximately $2,312.62 for 10 years.
Option 2: Monthly payments until death (14 more years)
n = 14 years * 12 months/year = 168 months
PV = PMT * (1 - (1 + 0.04167%)^(-168)) / 0.04167%
$250,000 = PMT * (1 - (1 + 0.04167%)^(-168)) / 0.04167%
Solving for PMT:
PMT = $250,000 * (0.04167%) / (1 - (1 + 0.04167%)^(-168))
PMT ≈ $1,290.42
Option 2 will provide monthly payments of approximately $1,290.42 until death (assuming 14 more years).
Option 3: Monthly payments until both you and your spouse die (22 more years)
n = 22 years * 12 months/year = 264 months
PV = PMT * (1 - (1 + 0.04167%)^(-264)) / 0.04167%
$250,000 = PMT * (1 - (1 + 0.04167%)^(-264)) / 0.04167%
Solving for PMT:
PMT = $250,000 * (0.04167%) / (1 - (1 + 0.04167%)^(-264))
PMT ≈ $1,045.34
Option 3 will provide monthly payments of approximately $1,045.34 until both you and your spouse die (assuming 22 more years).
You have a policy with a cash value of $250,000 which you wish to annuitize. You are currently 62 years old and your spouse is 58. Interest rates are 5% per year, and you are considering receiving monthly payments under three options: In option 1 you will receive 10 years of monthly payments.
With option 2 you will receive a monthly payment until you die (assuming 14 more years, according to the Mortality Table)
With option 3 you will receive a monthly payment until both you and your spouse die (assuming 22 more years).
How much will you receive with each option (ignoring administrative costs and fees)?
1 answer