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)?
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).
To calculate the monthly payment for each option, we will need to use the present value of an annuity formula. The formula is as follows:
PV = PMT * [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value of the annuity
PMT = Monthly payment
r = Interest rate per period (monthly interest rate in this case)
n = Number of periods (number of months in this case)
Option 1: 10 years of monthly payments
To calculate the monthly payment for option 1, we will use the formula with n = 10 * 12 = 120 months:
PV = $250,000
r = 5% per year / 12 = 0.4167% per month
PMT1 = PV * r / [1 - (1 + r)^(-n)]
PMT1 = $250,000 * 0.004167 / [1 - (1 + 0.004167)^(-120)]
PMT1 ≈ $2,639.72
Option 2: Monthly payment until you die (assuming 14 more years)
To calculate the monthly payment for option 2, we will use the formula with n = 14 * 12 = 168 months:
PMT2 = PV * r / [1 - (1 + r)^(-n)]
PMT2 = $250,000 * 0.004167 / [1 - (1 + 0.004167)^(-168)]
PMT2 ≈ $1,619.53
Option 3: Monthly payment until both you and your spouse die (assuming 22 more years)
To calculate the monthly payment for option 3, we will use the formula with n = 22 * 12 = 264 months:
PMT3 = PV * r / [1 - (1 + r)^(-n)]
PMT3 = $250,000 * 0.004167 / [1 - (1 + 0.004167)^(-264)]
PMT3 ≈ $1,207.65
Therefore, the approximate monthly payments for each option are:
Option 1: $2,639.72
Option 2: $1,619.53
Option 3: $1,207.65