Future Value of Annuity
Future value of regular equal payments.
Formula
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Example
Saving $100/month at 1%/month for 12 months yields about $1268.
How it works
This formula gives the accumulated value of a stream of equal payments made at regular intervals when each payment earns compound interest after it is deposited. It works because each deposit has a different amount of time to grow: the first payment compounds for all n periods, the next for n−1 periods, and so on, so the future value is the sum of a geometric series. The closed form P((1+r)^n−1)/r is just the compact result of adding those growing terms.
When to use it
Use this when you are making equal deposits into a savings account, retirement plan, sinking fund, or any investment that compounds at a fixed rate per payment period. It applies when payments are made at the end of each period; if payments are made at the beginning, a different adjustment is needed.
Worked example, step by step
Suppose you deposit $250 at the end of each month into an account earning 0.6% per month for 36 months. Step 1: Identify the values: P = 250, r = 0.006, n = 36 Step 2: Substitute into the formula: FV = 250 * ((1 + 0.006)^36 - 1) / 0.006 Step 3: Compute the growth factor: (1.006)^36 ≈ 1.231441 Step 4: Subtract 1: 1.231441 - 1 = 0.231441 Step 5: Divide by the rate: 0.231441 / 0.006 ≈ 38.5735 Step 6: Multiply by the payment: FV ≈ 250 * 38.5735 = 9643.38 Final answer: The future value is about $9,643.38.
Common mistakes to avoid
- Using the annual interest rate when the payments are monthly instead of converting to a monthly rate
- Forgetting that the formula assumes payments are made at the end of each period, not the beginning
- Plugging in a percent like 6 instead of the decimal rate 0.06
Did You Know?
Regular investing harnesses compounding — small monthly deposits can grow into a fortune over decades.
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