Annuity Calculator
An annuity calculator determines the regular payments from a lump sum investment or the lump sum needed to generate desired payments. Annuities convert savings into guaranteed income streams.
Annuity Payment Formula
Payment = Principal × (r × (1+r)^n) / ((1+r)^n - 1)
Where r = periodic rate, n = number of periods
Annuity Payments from Lump Sum
At 5% annual rate:
| Lump Sum | 10 Years | 15 Years | 20 Years | 25 Years |
|---|---|---|---|---|
| $100,000 | $12,950/yr | $9,634/yr | $8,024/yr | $7,095/yr |
| $250,000 | $32,375/yr | $24,085/yr | $20,060/yr | $17,738/yr |
| $500,000 | $64,750/yr | $48,170/yr | $40,120/yr | $35,476/yr |
| $1,000,000 | $129,500/yr | $96,340/yr | $80,240/yr | $70,952/yr |
Annuity Calculator Implementation
``javascript
function calculateAnnuityPayment(principal, rate, years) {
const r = rate / 100;
const n = years;
// Annuity payment formula
const payment = principal * (r * Math.pow(1 + r, n)) / (Math.pow(1 + r, n) - 1);
return {
annualPayment: payment.toFixed(2),
monthlyPayment: (payment / 12).toFixed(2),
totalPayments: (payment * years).toFixed(2),
interestEarned: ((payment * years) - principal).toFixed(2)
};
}
function calculateLumpSumNeeded(desiredPayment, rate, years) {
const r = rate / 100;
const n = years;
const lumpSum = desiredPayment * (Math.pow(1 + r, n) - 1) / (r * Math.pow(1 + r, n));
return {
lumpSumNeeded: lumpSum.toFixed(2),
desiredPayment,
years
};
}
console.log(calculateAnnuityPayment(500000, 5, 20));
// { annualPayment: '40120', monthlyPayment: '3343.33' }
`
Types of Annuities
Immediate annuities start payments right away. Deferred annuities grow tax-deferred before payouts begin. Fixed annuities guarantee rates; variable annuities tie to investments.
The Projection Behind This Page
Starting from $100,000, adding $200 a month at 5%:
| Year | Deposited | Balance | Growth | Growth on deposits |
|---|---|---|---|---|
| 1 | $102,400 | $107,572 | $5,172 | 5% |
| 5 | $112,000 | $141,937 | $29,937 | 27% |
| 10 | $124,000 | $195,757 | $71,757 | 58% |
| 20 | $148,000 | $353,471 | $205,471 | 139% |
After 20 years, 58% of the balance is growth rather than money you
put in. That crossover — the point where returns exceed contributions — is the whole reason
compounding is worth waiting for, and it arrives later than most people expect.The Formula
`
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
└── initial principal ──┘ └────── regular contributions ──────┘
`
The second term usually dominates. On these numbers the $200 monthly contribution
accounts for the larger share of the final balance, which is the practical lesson: how much
you add matters more than the rate, right up until the balance gets large.
How Long Until It Doubles
The Rule of 72 divides 72 by the rate to estimate doubling time. At 5%:
`
72 ÷ 5 = 14.4 years
`
The exact answer is 14.2 years — the rule is accurate to within a few months
for rates between 6% and 10%, and drifts at the extremes. It works because ln(2) ≈ 0.693 and
72 has convenient divisors.
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 yr | 35.0 yr |
| 5% | 14.4 yr | 14.2 yr |
| 7% | 10.3 yr | 10.2 yr |
| 10% | 7.2 yr | 7.3 yr |
| 15% | 4.8 yr | 5.0 yr |
Compounding Frequency at This Rate
A nominal 5% turns into a different effective yield depending on how often it
compounds:
| Compounded | Effective annual yield |
|---|---|
| Annually | 5.000% |
| Quarterly | 5.095% |
| Monthly | 5.116% |
| Daily | 5.127% |
| Continuously | 5.127% |
The gap between annual and monthly is worth having. The gap between monthly and daily is
0.011 percentage points — rounding. Compare accounts on
APY, which already folds the frequency in, rather than on the nominal rate.Inflation Is the Number That Matters
A 5% nominal return against 3% inflation is a 2.0% real return.
Real return is what buys anything:
`
real ≈ nominal − inflation
``
Over 14 years, 3% inflation cuts purchasing power by about 34%. A projection quoted in nominal dollars therefore overstates what the money will actually be worth, which is why retirement targets are usually stated in today's dollars.