Annuity Calculator

What is an annuity calculator?

An annuity calculator forecasts the growth of an investment during its accumulation phase. By combining a starting lump-sum principal with recurring annual or monthly additions and a steady growth rate, this tool projects the total accumulated balance and breaks down the split between your personal deposits and compound interest earnings.

Annuities are commonly used as long-term retirement planning vehicles. If you are comparing deferred annuities with workplace retirement plans, you can evaluate employer contributions using the 401(k) calculator. For government-backed social security pension schemes with guaranteed lifetime returns, check the Atal Pension Yojana calculator. For families setting aside funds for education over a multi-year horizon, the 529 plan calculator models compounding growth tailored to tuition milestones. To generate a custom lookup matrix of loan payment factors across interest rates and terms, use the annuity payment table. If you are analyzing debt schedules that rely on the inverse present value formula, check the amortization calculator or the EMI calculator.

Annuity Due vs. Ordinary Annuity

The timing of periodic deposits significantly impacts your ending balance due to the power of compounding:

• Annuity Due (Beginning of Period): Deposits are made at the start of each month or year. Because each contribution enters the account immediately, it earns interest throughout the entire payment interval, generating higher cumulative returns.
• Ordinary Annuity (End of Period): Deposits are made at the end of each payment period. Each contribution begins accruing interest in the subsequent cycle. This timing is typical for payroll deductions and mortgage payments.

Mathematical formulas for annuity accumulation

The total future value ($FV$) of an annuity portfolio equals the future value of the starting principal plus the future value of all periodic additions.

1. Future value of initial lump-sum principal:

2. Future value of an Ordinary Annuity (end of period additions):

3. Future value of an Annuity Due (beginning of period additions):

Where $P$ is starting principal, $r$ is the annual interest rate, $Y$ is total years, $PMT$ is the recurring payment per period, $i$ is the periodic interest rate, and $n$ is the total number of contribution periods.

Worked example of annuity growth

Suppose you begin with a $20,000 initial principal and deposit $10,000 at the beginning of each year (Annuity Due) for 10 years at a 6% annual return rate:

• Initial $20,000 principal compounds to $\$20{,}000 \times (1.06)^{10} = \$35{,}816.95$.
• Annual $10,000 additions compound to $\$10{,}000 \times \frac{(1.06)^{10} - 1}{0.06} \times 1.06 = \$139{,}716.43$.
• Total accumulated annuity balance: $\$35{,}816.95 + \$139{,}716.43 = \$175{,}533.38$.
• Total deposits: $\$20{,}000 + (10 \times \$10{,}000) = \$120{,}000$.
• Total compound interest earned: $\$175{,}533.38 - \$120{,}000 = \$55{,}533.38$.

Frequently asked questions