Future Value Interest Factor of Annuity (FVIFA) Calculator

The future value interest factor of annuity (FVIFA) tells you how much a series of $1 payments — one per period — will accumulate to at a fixed compound interest rate. It is the annuity counterpart of FVIF: where FVIF values a single lump sum, FVIFA values a stream of equal periodic contributions.

Use the calculator above to find the FVIFA for any rate and period count, then read on for the formula, worked examples, and practical applications.

What FVIFA Measures

FVIFA is the total future value of $n$ payments of $1 each, made at the end of every period, when each payment compounds at rate $r$ until the end of the final period. Because it is based on $1 payments, it works as a pure multiplier:

If FVIFA is 12.5779, then $500 deposited at the end of every year for 10 years at 5% grows to $500 × 12.5779 = $6,288.95. The factor encodes all the compounding math; you just multiply by the payment size.

The Formula

Where:

• $r$ is the interest rate per period in decimal form (e.g., 5% → 0.05).
• $n$ is the number of periods.

When $r = 0$, the formula is undefined (division by zero), but the result is simply $n$ — with no interest, the future value is just the sum of all payments.

How It Works

Each $1 payment compounds for a different number of remaining periods:

• The first payment compounds for $n - 1$ periods → $(1 + r)^{n-1}$
• The second payment compounds for $n - 2$ periods → $(1 + r)^{n-2}$
• …
• The last payment compounds for 0 periods → $(1 + r)^{0} = 1$

FVIFA is the sum of this geometric series, which simplifies to the formula above.

Quick Examples

At 5% for 10 periods, each dollar of periodic payment accumulates to $12.58. At 10% for 30 periods, each dollar becomes over $164 — the power of compound interest applied to repeated contributions.

Relationship to Other Factors

FVIFA is derived from FVIF and is closely related to the other time-value factors:

Notice that FVIFA = (FVIF − 1) / $r$, and PVIFA = FVIFA / FVIF. All four factors share the same $(1 + r)^{n}$ core.

Using the Calculator

1. Enter the interest rate as a percentage (e.g., 5 for 5%). The calculator converts it to decimal internally.
2. Enter the number of periods. These can be years, months, quarters — any consistent period, as long as the rate matches.
3. Read the FVIFA, displayed to four decimal places.
4. Multiply by your periodic payment to get the future value of the annuity. For example, if FVIFA is 12.5779 and you deposit $200 per period, the future value is $2,515.58.

Rate and Period Must Match

If you have an annual rate but monthly payments, either:

• Divide the annual rate by 12 and use the number of months as the period count, or
• Convert to an effective annual rate first and use years.

Mixing an annual rate with a monthly period count will produce incorrect results.

Ordinary Annuity vs. Annuity Due

The FVIFA formula above assumes an ordinary annuity — payments occur at the end of each period. If payments occur at the beginning of each period (annuity due), multiply FVIFA by $(1 + r)$:

The annuity due factor is always larger because each payment earns one extra period of interest.

Practical Applications

• Retirement savings. If you contribute $500/month for 30 years at 7% annual (0.583% monthly), FVIFA tells you the accumulation factor. Multiply by $500 to project your nest egg.
• Sinking funds. A company setting aside equal annual payments to retire a bond issue uses FVIFA to determine how much each payment needs to be.
• Education funds. Parents making regular deposits for a child's college fund can use FVIFA to estimate the total at enrollment time.
• Comparing options. Two savings plans with different rates and horizons yield different FVIFA values — the higher FVIFA means more accumulation per dollar contributed.

Limitations

• Fixed rate only. FVIFA assumes a constant rate every period. For variable rates, you need to compute each period's accumulation individually.
• Equal payments. All payments must be identical. For irregular contributions, FVIFA does not apply — use a period-by-period calculation instead.
• Nominal, not real. FVIFA does not adjust for inflation. Use a real interest rate (nominal minus inflation) to get inflation-adjusted projections.
• No taxes or fees. Real-world returns are reduced by taxes, management fees, and transaction costs. FVIFA gives gross accumulation; net results will be lower.

Frequently Asked Questions

What is the difference between FVIFA and FVIF?

FVIF is for a single lump-sum payment — how much $1 today grows to. FVIFA is for a series of equal payments — how much $1 per period accumulates to. Use FVIF for one-time investments; use FVIFA for regular contributions like monthly deposits.

What happens when the interest rate is 0%?

With no interest, no compounding occurs, so each $1 payment stays at $1. The total is simply the number of payments: FVIFA = $n$. The calculator handles this case automatically.

Can I use FVIFA for monthly contributions?

Yes, but the rate and period must match. For a 6% annual rate with monthly contributions, enter 0.5 (which is 6 ÷ 12) as the rate and use the number of months as the period count.

How do I calculate the required periodic payment for a target amount?

Rearrange the formula: Payment = Target Amount ÷ FVIFA. For example, to accumulate $100,000 in 20 years at 5%, FVIFA is 33.0660, so the required annual payment is $100,000 ÷ 33.0660 = $3,024.

Why does FVIFA grow so much faster than FVIF?

Because FVIFA represents the accumulation of many compounding payments, not just one. Each new payment starts compounding from its own deposit date, and the total is the sum of all those compounding chains.