Model retirement income with flexible joint survival assumptions. Test ages, terms, and discount settings easily. Review payments, factors, and outputs with simple steps today.
| Age A | Age B | Frequency | Survivor % | Guarantee | Initial Payment | Premium | Annuity Factor | Payout Rate |
|---|---|---|---|---|---|---|---|---|
| 67 | 63 | Monthly | 50% | 10 years | 1,200.00 | 175,000.00 | 196.067848 | 6.1203% |
This calculator uses a period-by-period survival model. It estimates each life separately. Then it combines them into one expected payment stream.
Step 1: Annual mortality at each future age is estimated as q(t) = q0 × (1 + m)^t.
Step 2: Period mortality is q(period) = 1 − (1 − q(t))^(1/f).
Step 3: Survival is built recursively with p(t+1) = p(t) × (1 − q(period)).
Step 4: After any guarantee period, expected payment multiple = pA × pB + s × [pA × (1 − pB) + pB × (1 − pA)]. Here, s is the survivor percentage.
Step 5: Present value factor = Σ expected payment multiple × growth factor × discount factor.
Step 6: Initial payout rate = payment frequency ÷ annuity factor.
This is a math-based approximation. It is useful for comparison, sensitivity testing, and structured retirement modeling.
A joint life annuity rate shows how much income a shared contract can support. It links premium, payment size, and survival risk. A higher rate means more early income for each unit of premium. A lower rate often reflects longer expected payments or stronger survivor protection.
Age is the first driver. Younger lives usually produce a larger present value factor. That reduces the payout rate. Older lives often reduce the factor. That raises the initial rate. Discount rate also matters. A higher discount rate lowers the value of future payments. That can raise the rate. Escalation works in the opposite direction. Rising payments cost more in present value terms.
Survivor percentage is another important lever. A 100 percent survivor benefit keeps income at the same level after the first death. That increases expected value. A 50 percent survivor option lowers future income after one death. That usually lowers cost and raises the initial payout rate. Guarantee years also matter. A long guarantee pays even if both lives die early. That makes the annuity more valuable.
The annuity factor is the present value of one unit of payment per period. Multiply it by the payment per period to estimate required premium. Divide premium by the factor to estimate a fair periodic payment. The payout rate converts that relationship into a yearly percentage. It is useful for comparing different structures quickly.
The schedule preview helps you inspect the math. Survival probabilities decline over time. Discount factors also decline over time. Growth factors rise when escalation is positive. The payment multiple stays at one during the guarantee period. After that, it reflects joint survival and the selected survivor share. This makes the calculator practical for education, retirement planning drafts, product comparisons, and scenario testing.
It is the present value of one payment unit per period. Multiply that factor by your chosen payment amount to estimate the required single premium.
It is the initial annualized payment divided by the premium. The calculator derives it from payment frequency and the computed annuity factor.
Each life can have a different starting mortality assumption and growth path. That gives you more control during sensitivity testing and comparison work.
It sets the payment share that continues after the first death. A larger survivor percentage usually lowers the initial payout rate.
It forces payments for the selected number of years, even if both annuitants die early. Longer guarantees increase present value.
Use it for mathematical modeling, comparison, and education. Real pricing normally uses detailed actuarial tables, expenses, profit margins, and regulation.
Beginning-of-period payments are discounted for less time. That increases present value and can reduce the fair initial payout rate.
CSV includes the full schedule for analysis. PDF is a shorter report meant for summary review and quick sharing.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.