Hong Life CalculatorsUnderstanding the annuity payout calculator — concept and principle
An immediate annuity turns a lump sum (the premium) into a stream of regular payments that starts right away. This calculator estimates the monthly payment a premium can support for a chosen number of years at a given interest rate, with an option for payments that grow each year. It also shows the annual payout, the total you would receive, how many months it takes to get the premium back, and the payout rate. Use it to sanity-check quotes.
How it is calculated
- Monthly rate i = (1 + annual rate)^(1/12) − 1, so the annual rate is treated as an effective yearly rate
- Monthly growth g = (1 + growth rate)^(1/12) − 1; number of payments N = years × 12
- Level payment (g = 0): A = P × i ÷ (1 − (1 + i)^−N)
- Growing payment: A = P × (i − g) ÷ (1 − ((1 + g) ÷ (1 + i))^N), the first payment, rising each month
- Total received = sum of all payments; payout rate = A × 12 ÷ P
Payments are assumed at the end of each month. The calculator works in whatever currency you pick.
The principle
The premium must equal the present value of all future payments. Each payment is discounted back to today at the interest rate; the formula above is the closed form of that sum, the same one used for mortgage payments, just seen from the other side. While the balance is large it earns interest, so the total paid out exceeds the premium. With growth, the starting payment is lower so that later, larger payments can still be funded.
Worked example
Default: $200,000 premium, 4.5% rate, 22 years, no growth.
- Monthly rate: 1.045^(1/12) − 1 ≈ 0.0036748; N = 22 × 12 = 264.
- Payment: 200,000 × 0.0036748 ÷ (1 − 1.0036748^−264) ≈ $1,184.85 per month.
- Annual payout: 1,184.85 × 12 ≈ $14,218.
- Total received: 1,184.85 × 264 ≈ $312,801.
- Payback: 200,000 ÷ 1,184.85 ≈ 168.8, so the 169th payment recovers the premium. Payout rate: 14,218 ÷ 200,000 ≈ 7.11%.
How to read the result
The payout rate is not an interest rate; part of every payment is your own principal coming back. A real life-contingent annuity is priced by an insurer using mortality tables, expenses and profit, and it pays for as long as you live, so quotes can be higher or lower than this fixed-term figure. Compare several offers at the same premium.
Common mistakes
- Comparing a payout rate with a bond yield as if both were pure interest.
- Ignoring inflation: a level $1,185 buys noticeably less after 20 years.
- Forgetting fees, surrender terms and the insurer's financial strength.
Frequently asked questions
How much does a $200,000 annuity pay per month?
At 4.5% over 22 years, about $1,185 a month in this model. Insurer quotes for lifetime annuities vary with age and gender.
Why is the total received more than the premium?
The money not yet paid out keeps earning interest, and that interest is paid to you.
What does payment growth do?
It starts the payment lower and raises it each year, which helps offset inflation.
Sources: Standard financial mathematics: present value of an ordinary annuity and of a growing annuity (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)