Future Value of an Annuity: A Five-Payment Example

Set a valuation date and deposit schedule

This example values five deposits of 2,000 made at the ends of five successive years, with a constant 4% annual growth assumption. The valuation date is immediately after the fifth deposit. The first deposit therefore grows for four years, while the fifth is included at its original amount. A regular deposit stream is an annuity calculation. A single-lump-sum Future Value Calculator cannot directly represent the five different deposit dates with one present-value input; the site's Annuity Calculator is the appropriate tool for this annual ordinary stream.

Add the individual future values

The first 2,000 becomes 2,000×1.04^4=2,339.71712 at the valuation date. The second becomes 2,249.728, the third 2,163.20, the fourth 2,080 and the fifth remains 2,000. Their sum is 10,832.64512, or 10,832.65 rounded to two decimals. Total deposits are 10,000 and modeled growth is 832.64512. Listing the five terms reveals the timing clearly and provides a direct check on the compact formula. Keep the terms unrounded until the final sum to avoid introducing small accumulation errors.

Verify the compact formula in the tool

Ordinary-annuity future value is P×[((1+i)^n−1)/i]. With P=2,000, i=0.04 and n=5, the bracketed factor is 5.41632256, so the result is 10,832.64512. Enter payment 2000, annual rate 4 and years 5 to reproduce the displayed 10,832.65. The tool also reports the 10,000 total contribution. Its rate remains constant throughout the example. The formula describes that assumption; it does not forecast a market return or guarantee that an actual savings product will earn the supplied rate for the entire period.

Compare with investing the whole amount immediately

If all 10,000 were available and invested at time zero for five years, the single-lump-sum future value would be 10,000×1.04^5=12,166.529024. That is higher because the entire amount is invested earlier. It is not an alternative calculation of the same contribution schedule. Conversely, depositing 10,000 only at the end of year five produces no growth before the chosen valuation date. The beginning amount, deposit dates and valuation date must all remain aligned when comparing outputs from a lump-sum calculator and an annuity calculator.

Solve for the annual deposit needed for a target

Suppose the desired value at the same time-five date is 12,000. Divide the target by the ordinary-annuity factor: 12,000/5.41632256, approximately 2,215.53 per year. Retain more digits when checking an exact target, because five deposits rounded to cents can produce a small final difference. If deposits must be whole currency units and the target is a minimum under the stated assumptions, round upward and recalculate. A target-solving calculation changes the payment amount while preserving the rate, payment count and timing convention.

Move the deposits to the beginning of each year

If the same five 2,000 payments arrive at times 0 through 4 instead of 1 through 5, each has one extra year of growth before time 5. Multiply 10,832.64512 by 1.04 to obtain 11,265.9509248, or 11,265.95. This is an annuity due. The local annual Annuity Calculator has no due selector, so the additional multiplication must be performed separately. The monthly SIP Calculator uses a different schedule and rate conversion; it is not a direct replacement for this five-payment annual example.

Check the assumptions before reusing the result

At zero return, five payments of 2,000 simply total 10,000, which checks the deposit count. If contributions rise, pause or occur irregularly, calculate each payment's accumulated value from its own date. Fees and taxes are absent from this example, and inflation changes what the final amount can purchase. Document whether the supplied rate is intended before or after those effects. The result answers a specific savings arithmetic question under a fixed annual model; it does not choose a product or establish the affordability of the recurring deposit.

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