🏦 Compound Savings Calculator

Why use this calculator?

Compound interest is the one piece of arithmetic that decides what saving does, and it is invisible on a single bank statement: the interest paid next year depends on the interest already added. This calculator grows a balance at a fixed rate with money going in regularly, so you can see what a term deposit, a savings account or a house deposit plan actually comes to. It also answers the question a savings account never spells out: how much of the final figure is money you put in, and how much of it the bank did.

The surprising side of compounding

A few facts about the piece of arithmetic the whole page rests on:

• A penny doubled every day for 30 days comes to $10,737,418.24, and nearly all of it arrives at the end: on day 20 the penny is still only $10,485.76, and the final day adds more than the twenty-nine before it put together.
• The rule of 72 is the shortcut worth memorising: money doubles in roughly 72 ÷ the rate, in years. At 6% it predicts 12 years, and the exact answer is 11.90.
• Time does more of the work than the rate does. $10,000 left alone at 7% for 40 years becomes about $149,745 with nothing added — nearly fifteen times the money, and nearly four times what the same $10,000 comes to in twenty years at the same rate.
• Compound interest is old enough to have a printing history: tables for it were being published by Italian merchants in the 1340s, and one of the earliest books devoted to the subject was Richard Witt’s Arithmeticall Questions in 1613.

How does this calculator work?

Interest is worked out at the rate that matches the compounding you chose, and added to the balance each time it comes round:

interest for one period = balance × (rate ÷ 100 ÷ periods per year)

so 5% compounded monthly is 5% ÷ 12 each month, worked out on a balance that has already grown by every earlier lot. Over a whole term that is the familiar equation, where the money goes in and nothing comes out:

A = P × (1 + r ÷ m)^(m × t)

with P the starting balance, r the yearly rate, m how many times a year interest is added and t the term in years. Regular deposits turn it into a sum rather than one figure, so the term is stepped through in units that suit both frequencies at once — a daily rate with weekly deposits is counted in 1/18,980ths of a year, so nothing drifts out of line:

• Interest builds up on the balance as time passes and is added at each compounding point, which is why a "per annum" rate still moves the balance the moment the period turns over.
• A deposit made part-way through a period earns a share of that period's interest, and a deposit at the start of a period earns a little more than the same deposit at the end of it, because it is there for longer.
• The final balance includes interest that has built up but has not been added yet, so a term ending mid-way through a compounding period is not short-changed.
• The effective yearly rate is (1 + rate ÷ 100 ÷ m)^m − 1: the rate with compounding folded in, which is the figure to compare one account with another.

Frequently asked questions