Accumulated Value Formula in 2 Easy Steps
Accumulated value is the total an investment builds up to over time: the original principal plus all the interest it earns. It is the term many textbooks and actuarial courses use for future value, and it boils down to two quick steps.
Accumulated value explained simply
Accumulated value is principal plus all the interest it earns: A = P × (1 + r)ⁿ, and interest = A − P. In the example, $2,000 at 6% for 4 years accumulates to about $2,524.95, of which $524.95 is interest.
What this accumulated value lesson covers
- What accumulated value means and how it relates to future value
- The accumulation factor and where it comes from
- A two-step method: build the factor, then multiply
- How to split the answer into principal and interest
Accumulated value formula, explained
- A
- accumulated value
- P
- principal invested
- r
- interest rate per period
- n
- number of periods
- A
- accumulated value
- P
- principal
How to calculate accumulated value in 2 steps (worked example)
You invest $2,000 at 6% a year for 4 years. What is the accumulated value, and how much of it is interest?
- Step 1, the accumulation factor: (1.06)⁴ ≈ 1.262477.
- Step 2, multiply by the principal: A = $2,000 × 1.262477 ≈ $2,524.95.
- Interest earned = $2,524.95 − $2,000 = $524.95.
Answer: Accumulated value ≈ $2,524.95, of which $524.95 is interest (rounded to the cent).
Accumulated value vs future value vs present value
| Accumulated value | Future value | Present value | |
|---|---|---|---|
| Direction | Today → later | Today → later | Later → today |
| Where you see the term | Actuarial and some textbooks | Most finance courses | Most finance courses |
| Formula | P × (1 + r)ⁿ | PV × (1 + r)ⁿ | FV ÷ (1 + r)ⁿ |
Harder accumulated value questions
What if you also deposit $1,000 at the end of Year 2?
Accumulate each deposit separately and add: $2,000 grows to $2,524.95 and the $1,000 grows for 2 years to $1,123.60, for a total of about $3,648.55.
How much of the interest is 'interest on interest'?
Simple interest would give 2,000 × 6% × 4 = $480. Compound interest gives $524.95, so about $44.95 is interest earned on earlier interest.
Common accumulated value questions
What is the accumulated value formula?
With compound interest, accumulated value A = P × (1 + r)ⁿ, where P is the principal, r is the rate per period and n is the number of periods. With simple interest it is A = P × (1 + r × n).
Is accumulated value the same as future value?
For a single deposit, yes. Both describe what money grows to after earning interest. Accumulated value is the wording common in actuarial and interest theory courses, while future value is the usual corporate finance term.
What is an accumulation factor?
It is the (1 + r)ⁿ part of the formula: what $1 grows to after n periods at rate r. Multiply it by any principal to get the accumulated value. At 6% for 4 years the factor is about 1.2625.
How do you find accumulated value with several deposits?
Accumulate each deposit separately to the same end date using its own number of periods, then add the results. If the deposits are equal and regular, the future value of an annuity formula does the same job faster.