Future Value of an Ordinary Annuity: Formula & Examples
The future value of an ordinary annuity is the total balance that equal end-of-period payments grow to, including interest. Use FV = R × [((1 + i)ⁿ − 1) ÷ i], where R is the payment, i the rate per period, and n the number of payments. So $2,400 deposited each year-end for four years at 4% grows to $10,191.51.
This helps accounting students determine how repeated deposits build a fund for a future expenditure. The timing matters: a deposit made later has less time to grow. New to this topic? Start with the time value of money in accounting. This lesson assumes the payment interval matches the compounding interval, a constant positive rate, and no starting balance, fees, or taxes.
Watch: calculating and adding the future values of equal payments
This clip runs from 6:30 to 13:38 of the full lecture. At 6:30, you’ll add up each payment’s future value by hand. At 8:32, you’ll see the factor formula and financial tables.
What makes a payment series an ordinary annuity?
An annuity is a sequence of equal cash payments or receipts separated by equal time intervals. In an ordinary annuity, each payment occurs at the end of its interval. The word “rent” sometimes means the periodic payment in a textbook problem; it does not necessarily refer to renting property.
For four annual payments, the cash arrives at times 1, 2, 3, and 4. We measure future value at time 4, immediately after the final payment. If payments start today instead, review ordinary annuity vs annuity due. A single initial deposit uses a different calculation: future value of a single sum.
If the first payment is pushed back several periods, read about the deferred annuity.
| Time | 0 (today) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Deposit | None | $2,400 | $2,400 | $2,400 | $2,400 |
| Years of growth to time 4 | Not applicable | 3 | 2 | 1 | 0 |
What is the formula for the future value of an ordinary annuity?
| Symbol | Meaning | Use in the calculation |
|---|---|---|
| FV | Future value | The full accumulated balance on the specified date. |
| R or PMT | Periodic payment | One payment, not the total of all payments. |
| i | Interest rate per period | Use 0.04 for 4% per payment interval. |
| n | Number of payments | Four annual payments means n = 4. Textbooks may call n the number of compounding periods. The two match here because payments and compounding share the same interval. |
FV = payment × ordinary annuity factor
The factor adds up how much each $1 payment grows to by the end date. The first payment earns interest for n − 1 periods; the last earns no interest before the measurement date. Even so, use n, not n − 1, in the annuity formula. The California State Board of Equalization provides the same future-worth-of-one-per-period formula.
Worked example: four year-end deposits
Hypothetical example. Cedar Workshop deposits $2,400 at the end of each of four years. The fund earns 4% compounded annually. Find the balance immediately after the fourth deposit.
= $2,400 × 4.246464 = $10,191.51
| Deposit date | Years of growth | Value at end of Year 4 |
|---|---|---|
| End of Year 1 | 3 | $2,400 × 1.04³ = $2,699.67 |
| End of Year 2 | 2 | $2,400 × 1.04² = $2,595.84 |
| End of Year 3 | 1 | $2,400 × 1.04 = $2,496.00 |
| End of Year 4 | 0 | $2,400.00 |
| Total | $10,191.51 |
Contributions total $9,600. Interest is therefore $10,191.51 − $9,600 = $591.51. The future value of an ordinary annuity includes both components. Amounts in the table are displayed to cents; retain full precision until the final answer.
How do you use a future value annuity table?
Select the table titled “future value of an ordinary annuity of 1.” Find the four-payment row and 4% column. The factor is 4.246464, or 4.24646 in a five-decimal table. Multiply by one $2,400 payment. Do not select the single-sum table, which values only one deposit.
Here is a short version of that table.
| Periods (n) | 3% | 4% | 5% | 6% |
|---|---|---|---|---|
| 1 | 1.00000 | 1.00000 | 1.00000 | 1.00000 |
| 2 | 2.03000 | 2.04000 | 2.05000 | 2.06000 |
| 3 | 3.09090 | 3.12160 | 3.15250 | 3.18360 |
| 4 | 4.18363 | 4.24646 | 4.31013 | 4.37462 |
| 5 | 5.30914 | 5.41632 | 5.52563 | 5.63709 |
| 6 | 6.46841 | 6.63298 | 6.80191 | 6.97532 |
| 10 | 11.46388 | 12.00611 | 12.57789 | 13.18079 |
A table factor already combines all four payments. Multiplying the result by four again would count the deposits repeatedly. Small differences between table and calculator answers come from rounding. Here, $2,400 × 4.24646 = $10,191.50, while the calculator gives $10,191.51.
How do you handle semiannual or monthly payments?
Hypothetical example. A business deposits $1,500 at each half-year end for three years at a 6% nominal annual rate compounded semiannually. Each interval earns 3%, and there are six payments. The future value of an ordinary annuity is $1,500 × [(1.03⁶ − 1) ÷ 0.03] = $9,702.61.
Use i = 6% ÷ 2 and n = 3 × 2. This division applies to a stated nominal rate with semiannual compounding; do not automatically divide an effective annual rate. Review compounding periods and rate conventions if the units are unclear.
Monthly payments work the same way. Hypothetical example. A student saves $300 at the end of each month for two years at 6% compounded monthly. Each month earns 0.5%, and there are 24 payments.
FV = $300 × [(1.005²⁴ − 1) ÷ 0.005] = $7,629.59
The student deposits $7,200, so interest is $429.59. In Excel, use =FV(6%/12,24,-300,0,0).
How do you calculate it in Excel?
For Cedar Workshop, =FV(4%,4,-2400,0,0) returns $10,191.51. The payment is negative because it leaves the depositor; the future balance is positive. Present value is zero, and the final zero specifies end-of-period payments. Microsoft documents these inputs in its FV function reference.
How does this show up in accounting?
In accounting, this calculation often supports a sinking fund. A sinking fund is money set aside in regular deposits to pay a future cost, such as replacing equipment or retiring bonds.
Suppose Cedar Workshop’s deposits go into an equipment replacement fund. This schedule shows how the balance builds.
| Year | Beginning balance | Interest at 4% | Deposit | Ending balance |
|---|---|---|---|---|
| 1 | $0.00 | $0.00 | $2,400.00 | $2,400.00 |
| 2 | $2,400.00 | $96.00 | $2,400.00 | $4,896.00 |
| 3 | $4,896.00 | $195.84 | $2,400.00 | $7,491.84 |
| 4 | $7,491.84 | $299.67 | $2,400.00 | $10,191.51 |
| Total | $591.51 | $9,600.00 |
The ending balance ties to the formula answer. Here are the Year 3 entries.
Record the interest:
Debit Equipment Replacement Fund $195.84
Credit Interest Revenue $195.84
Record the deposit:
Debit Equipment Replacement Fund $2,400.00
Credit Cash $2,400.00
Common mistakes
- Compounding every deposit for four years. The deposits arrive on different dates. For Cedar Workshop, this wrong approach gives $9,600 × 1.04⁴ = $11,230.64.
- Adding deposits without interest. $9,600 is contributed principal, not the accumulated balance.
- Using n − 1 in the formula. That drops a payment. For Cedar Workshop, $2,400 × [(1.04³ − 1) ÷ 0.04] gives only $7,491.84.
- Choosing the annuity due table. Beginning-of-period deposits earn one extra period, so you would get $10,599.17 instead of $10,191.51.
- Using the wrong unknown. When the target balance is supplied, use future value annuity problems for payments or periods to work backward.
Interactive exercise: future value of an ordinary annuity
Practice deposit timing, interest periods, and the future value factor of an ordinary annuity with six dropdown questions.
Review: How is the future value of an ordinary annuity determined?
Compute the value to which each rent in the series will accumulate, then total the individual future values.
When do ordinary annuity rents earn interest?
Rents are deposited at the end of each period, so they earn no interest during the period in which they are deposited. In the five-period example, the third rent earns interest for only two periods: periods four and five.
What is the future value factor formula?
Future value factor = ((1 + i) raised to n, minus 1) divided by i.
- FVF-OAn,i
- Future value factor of an ordinary annuity.
- i
- Rate of interest per period.
- n
- Number of compounding periods.
Exercise scenario: For the five-period timing question, assume one equal deposit at the end of each of five periods. Measure future value immediately after the fifth deposit. Payment and compounding intervals match, and the interest rate per period is positive.
Select one answer for each question, then choose Check answers. Review the feedback, revise your answers, or choose Start again for another attempt.
Ordinary annuity rents are deposited at the end of the period.
It earns no interest during that period because it is deposited at the end.
The third rent earns interest for two periods: four and five. It earns none in period three.
Total the individual future values to determine the annuity’s future value.
The symbol i represents the rate of interest per period.
The symbol n represents the number of compounding periods.
Ready to apply the concepts? Continue to the three calculation practice questions with answers.
Three practice questions with answers
These questions are hypothetical. Assume constant rates, retained interest, and no fees or taxes.
1. Calculate future value
Three $800 deposits occur at year-end and earn 5% annually. What is the balance just after deposit three?
$2,522.00. The factor is (1.05³ − 1) ÷ 0.05 = 3.1525. Multiply it by $800. The last payment earns no interest.
2. Count the periods
There are six annual year-end deposits. How many years does the first deposit grow, and what is n in the annuity formula?
Five years of growth; n = 6. The first deposit occurs at time 1 and is measured at time 6. The annuity formula still counts all six payments.
3. Use a semiannual rate
Four half-year-end deposits of $1,250 earn 4% nominal annual interest compounded semiannually. Find future value.
$5,152.01. Use 2% per half-year and four payments: $1,250 × [(1.02⁴ − 1) ÷ 0.02].
Frequently asked questions
Why does the final ordinary-annuity payment earn no interest?
It is deposited on the measurement date. No time passes between that deposit and the stated future value.
Does an annuity have to be annual?
No. Payments can be monthly, quarterly, or semiannual. Here, the interest period and payment interval must match.
What if payments and compounding happen on different schedules?
Convert the rate to the payment interval first. For $1,000 at each half-year end for two years at 8% compounded quarterly, the quarterly rate is 2%, so the half-year rate is 1.02² − 1 = 4.04%. With n = 4, FV = $1,000 × [(1.0404⁴ − 1) ÷ 0.0404] = $4,248.99.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period, and an annuity due pays at the beginning. Each annuity due payment earns one extra period of interest, so its future value is the ordinary annuity answer × (1 + i). For Cedar Workshop, that is $10,191.51 × 1.04 = $10,599.17.
How do you calculate the future value of an ordinary annuity in Excel?
Use =FV(rate, nper, pmt, pv, type). For Cedar Workshop, =FV(4%,4,-2400,0,0) returns $10,191.51. Enter the payment as a negative number, and use 0 for type because ordinary annuity payments come at the end of the period.
Where is this calculation used in accounting?
It is common with sinking funds, which are regular deposits set aside to pay a future cost, such as retiring bonds or replacing equipment.
What if the interest rate is zero?
Future value equals payment × number of payments. Use that direct calculation because the displayed factor formula would divide by zero.
Key takeaways
- An ordinary annuity has equal payments at the end of each period.
- FV = R × [((1 + i)ⁿ − 1) ÷ i], with i and n matched to the payment interval.
- The first payment earns n − 1 periods of interest and the last earns none, but the formula still uses n.
- Cedar Workshop’s four $2,400 deposits at 4% grow to $10,191.51: $9,600 of deposits plus $591.51 of interest.
For more worked examples and practice, explore the Intermediate Accounting course.
About the author
Mansour Farhat, CPA, CIA, DBA, teaches accounting through Farhat Lectures, which offers courses for CPA, CMA, and EA exam candidates and accounting students. His YouTube channel has more than 280,000 subscribers.
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