Future Value of Annuity Calculator
Future value of equal monthly deposits with interest split.
What it does
An ordinary annuity is a stream of equal deposits made at fixed dates. Retirement savers meet it as monthly contributions, parents meet it as college fund transfers, and borrowers meet its mirror image in loan payments. The question is always the same: what will the pile be worth after the last deposit, with interest compounding along the way.
The tool above answers with three numbers. Future value is the balance at the end, paid-in total is deposits without growth, and interest earned is the gap between them. Defaults of $200 a month at 6% for 10 years give $32,775.87, of which $24,000.00 is deposits and $8,775.87 is interest. Seeing the split keeps expectations honest, because early years are mostly deposits and late years are mostly compounding.
The formula multiplies one deposit by a growth factor built from the monthly rate and the deposit count. A 6% nominal rate with monthly compounding means 0.005 a month for 120 months. Raise the rate by one point or stretch time by five years and the factor moves a lot; that sensitivity is why small fees compound into large losses over decades.
This page models deposits only, at month end, with a fixed rate and no withdrawals. It leaves out taxes, expense ratios, inflation, and irregular deposits. For a full plan, run this math first for the savings engine, then layer costs and taxes on top.
How to use
- Enter the equal monthly deposit in dollars.
- Enter the nominal annual rate in percent.
- Enter the number of years of deposits.
- Read the future value first, then the paid-in total.
- Compare interest earned against the paid-in total.
- Repeat with a lower rate to see how sensitive growth is to fees.
Formula
- PMT
- Equal deposit at the end of each month, in dollars.
- r
- Monthly rate as a decimal, from the nominal annual percent divided by 12.
- n
- Count of monthly deposits, years times 12.
Ordinary annuity means deposits land at the end of each month. With a zero rate there is no growth, so the value is deposits only. Taxes, fees, missed deposits, and rate changes are outside this math.
Worked example
Example: $200 a month for 10 years at 6%
Defaults: $200 monthly, 6% nominal annual with monthly compounding, 10 years, deposits at month end.
- Inputs: $200 a month, 6% annual, 10 years.
- Monthly rate: 0.06 / 12 is 0.005. Months: 10 times 12 is 120.
- Power: 1.005 to the 120th is 1.81939673.
- Factor: (1.81939673 minus 1) / 0.005 is 163.87935.
- Future value: 200 times 163.87935 is $32,775.87.
- Paid in: 200 times 120 is $24,000.00. Interest: $32,775.87 minus $24,000.00 is $8,775.87. Tool shows the same three numbers.
Reference table
| Deposits | Rate and time | Future value |
|---|---|---|
| $200 x 120 | 6%, 10 years | $32,775.87 |
| $100 x 60 | 5%, 5 years | $6,800.61 |
| $300 x 36 | 0%, 3 years | $10,800.00 |
| $500 x 240 | 7%, 20 years | $260,463.33 |
| $50 x 12 | 4%, 1 year | $611.12 |
Limits
- Equal monthly deposits at month end only. Irregular amounts need a schedule.
- Fixed nominal rate with monthly compounding. Variable rates need year by year math.
- Before tax, fees, and inflation. Real spending power is lower.
- No withdrawals or missed months. Gaps cut compounding fast.
Common mistakes
- Using the annual rate as the monthly rate, which overstates growth 12 times.
- Counting years as deposits instead of months.
- Pricing annuity due with the ordinary formula and missing one month of interest.
- Ignoring fees, then wondering why the statement trails the math.
- Comparing nominal and inflation adjusted results as if equal.
Try it yourself
Quick checks. Answers sit tucked under each question.
$100 a month, 5%, 5 years?
Rate 0.05/12 is 0.0041667, n is 60. FV is $6,800.61 on $6,000.00 paid, so $800.61 interest.
$300 a month, 0%, 3 years?
At 0%, FV is deposits only: 300 times 36 is $10,800.00, interest $0.00.
Questions
What is the formula for an ordinary annuity?
FV = PMT times ((1+r)^n minus 1) / r, with r the per period rate and n the count of deposits. Here r is 0.005 and n is 120.
How do annual rate and years become r and n?
Monthly rate is annual / 12 / 100 and months are years times 12. Here 6% gives 0.005 and 10 years gives 120 deposits.
What happens at 0% interest?
With r at zero the formula divides by zero, so the code uses FV = PMT times n. Here $300 for 36 months is $10,800.00.
What is the difference from annuity due?
Annuity due deposits at the start of each period, so each deposit compounds once more. Multiply the ordinary result by (1+r).
Does compounding frequency matter?
Nominal with monthly compounding here. If the bank compounds daily but takes monthly deposits, convert to an equivalent monthly rate first.
Is this my retirement balance?
No. This is deposits only, before tax, fees, and inflation. A retirement plan needs those layers added.
Sources
- OpenStax Principles of Finance: Annuities
- eCampusOntario Mathematics of Finance: Future Value of Annuities