Accumulated Value Formula in 2 Easy Steps

What you will learn

• 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

The formulas

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?

1. Step 1, the accumulation factor: (1.06)⁴ ≈ 1.262477.
2. Step 2, multiply by the principal: A = $2,000 × 1.262477 ≈ $2,524.95.
3. 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).

Common 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.