Compound a savings balance

How the savings calculator works

You enter the current balance, a regular top-up, whether that top-up is monthly or yearly, an annual interest rate, how often interest is credited, and the number of years. Tax is off unless you turn it on.

Each top-up is deposited at the start of the month or year. It earns interest only for the time it has been in the account. Interest is credited at the compounding frequency: annually, semiannually, quarterly, monthly, or daily. Daily mode uses a 365-day year and does not add a leap day.

When tax is on, it is a flat percentage of positive interest only. The default 30% matches the lower Finnish capital-income tax rate. The higher 34% bracket is not modeled, and a negative rate is not taxed.

Formula

Inside one compounding period the interest base is the balance at the start of the period plus each top-up multiplied by the fraction of the period it is present. Interest equals that base times the periodic rate. After tax, the balance increases by interest minus tax.

With no tax and monthly compounding, a starting balance P and a monthly top-up C at monthly rate i for N months ends at P×(1+i)^N + C×(1+i)×((1+i)^N−1)/i. That is the annuity-due form, because the deposit happens before that month's interest.

A worked example

Defaults: 10 000,00 € already saved, 200,00 € added at the start of each month, 2.5% interest compounded monthly, no tax, 20 years.

The balance ends at 78 803,15 €. You contributed 58 000,00 € in total, of which 20 803,15 € is interest.

Questions

When is the monthly deposit added?

At the start of each month, before that period's interest is credited. A yearly top-up is added at the start of each year.

Is the 30% tax always applied?

No. Tax is off until you enable it. When it is on, the default rate is 30% of positive interest. You can change the rate. Returno does not apply the Finnish 34% bracket.

What if the interest rate is zero?

The balance equals what you put in. No interest is credited and no tax is charged.