Savings & Planning, Explained

Saving money is simple to describe and hard to do consistently. The math, though, is on your side: money left to compound grows faster the longer you leave it. This guide covers the ideas behind every BedrockCalc savings calculator.

Why compound interest is called the eighth wonder

Compound interest means you earn interest on your interest. Each period, the interest earned is added to your balance, and the next period’s interest is calculated on that larger balance. Over long periods this snowballs.

• A lump sum grows by A = P(1 + r/m)^(m·t) — where P is the starting amount, r the annual rate, m the compounding periods per year and t the years.
• Regular contributions add an annuity term on top, so consistent monthly deposits can outgrow a big one-time deposit.
• The crossover moment — when total interest earned overtakes everything you deposited — is the whole point of investing early.

Time beats timing

Compound growth puts time in the exponent: each extra year multiplies the entire balance again, so the curve steepens the longer you stay in. Starting early is what buys you those steep later years.

• Starting ten years earlier routinely beats contributing twice as much later.
• The most common regret among savers is simply not starting sooner.
• Automate contributions — consistency matters more than picking the perfect moment.

Compounding frequency matters less than you think

Moving from annual to monthly compounding on a 5% account adds about 0.12 percentage points of effective yield; monthly to daily adds barely a hundredth more.

• When comparing savings accounts or CDs, look at the quoted APY, which already includes the compounding effect.
• Spend your attention on the rate and the fees instead.

Planning around goals

Different goals call for different tools, but the mechanics are the same:

• Emergency fund — aim for three to six months of essential expenses, held somewhere safe and liquid.
• A dated goal (a house deposit, a wedding) — work backwards from the target date to find the monthly amount required.
• College — costs inflate faster than general prices, so model the inflated future figure, not today’s sticker price.

What rate of return should you assume?

It depends on the account:

• High-yield savings and CDs currently pay roughly 4–5%.
• Diversified stock portfolios have averaged about 10% per year over the long run (≈7% after inflation).
• Bonds sit in between.

For planning, many people model 6–8% and treat higher numbers as optimistic. Whatever you choose, the two habits that amplify everything are automating your contributions and leaving the interest alone to compound.