Savings Calculator — regular deposits, compounding balance

How it works

Each deposit lands at the end of its period and starts compounding at r/k per period from then on — the earliest deposits compound longest, which is why the formula sums to d((1+r/k)^(k·y) − 1)/(r/k), the savings-annuity formula. The outputs split the result honestly: total deposited is d times the number of deposits, straight-line money you put in; interest earned is everything above it, the compounding's contribution. The years sweep runs your same deposit at 5, 10, 20, and 30 years — deposits double when time doubles, but the balance more than doubles, and watching the ratio drift upward is the whole argument for starting early.

Worked example

The default inputs are LibreTexts' published example: Tanya deposits $300 at the end of each quarter into an account earning 5.75% compounded quarterly. After 4 years — 16 deposits totalling $4,800 — the formula gives $5,353.89, about $554 of it interest. Stretch the same deposits to 30 years in the sweep and the interest share overtakes the deposits themselves: that shift is this calculator's arithmetic on the same published formula.

Frequently asked questions

How is a savings balance with regular deposits calculated?

With the savings-annuity formula: each deposit compounds from the period it lands, and the closed form d((1+r/k)^(k·y) − 1)/(r/k) sums them all. It is the same arithmetic a bank's statement performs, assuming end-of-period deposits and a constant rate.

How much of the final balance is interest?

The interest-earned output is exactly that split: balance minus everything deposited. Early on it is small — deposits dominate a young account — and it compounds into the larger share on long horizons, which the years sweep makes visible for your own numbers.

Does the deposit frequency matter?

Somewhat: more frequent deposits start compounding sooner, and the rate divides across more periods. But as with compounding frequency generally, the effect is modest next to the rate and the years — moving from annual to monthly deposits of the same annual total shifts the result far less than one extra year of saving.

What if I already have a starting balance?

This page models deposits only. A lump sum growing alongside deposits is the future-value calculator's job — it combines the compound growth of what you have with the annuity growth of what you add.

How do I find the deposit needed for a target amount?

Invert the question: the savings-goal calculator solves the same formula for d given the target, rate, and years — the "how much per month to reach $200,000" direction, with LibreTexts' published example as its anchor.

Is the interest taxed?

In ordinary accounts, commonly yes — interest is usually taxable in the year earned, which lowers the effective rate; tax-advantaged retirement accounts defer or exempt it. This page computes the pre-tax arithmetic; the account type decides the rest.

How accurate is this, and what does it exclude?

Exact for a constant rate, end-of-period deposits, and no withdrawals. It excludes rate changes, missed or extra deposits, fees, taxes, and inflation — the balance is in future dollars, worth less in purchasing power than the same figure today. Rates on real accounts float, so treat long horizons as scenarios, not forecasts.