Investing & Returns, Explained

Investing is the practice of putting money to work today so it is worth more later. The hard part is not the idea — it is comparing opportunities fairly. A 40% gain over five years and a 40% gain over one year are not the same thing. This guide explains the ideas behind every BedrockCalc investment calculator, in plain English, so you can project returns and put every opportunity on equal footing. It is educational, not personalized advice.

The time value of money

The single most important idea in finance is that a dollar today is worth more than a dollar tomorrow, because today’s dollar can be invested and earn a return. Every serious calculation rests on this. The Finance (TVM) calculator ties five variables together, and if you know any four, it solves for the fifth.

• N — the number of periods (often years, sometimes months).
• Rate (I/Y) — the interest or return rate per period.
• PV — present value, what the money is worth now.
• PMT — the recurring payment or contribution each period.
• FV — future value, what it grows to at the end.

The core relationship linking them is a single equation. In practice you rarely solve it by hand — you tell a solver which variable is unknown and it does the algebra. The Investment calculator is this same engine framed around a goal: how much a lump sum plus monthly contributions will grow to, or how much you would need to contribute to reach a target.

Present value vs future value

These are the same coin viewed from opposite ends of time.

• Future value answers: what will this grow into? The basic form is FV = PV(1+r)^n. Add a stream of contributions and you tack on an annuity term for the deposits.
• Present value answers: what is a future sum worth today? You run the formula in reverse — PV = FV / (1+r)^n — which is called discounting.
• Discounting a stream of future payments (like a pension or a rental income) uses the annuity form and is the heart of discounted cash flow analysis.
• The discount rate is a choice, and it matters enormously. A higher rate shrinks the present value of distant cash flows fast.

The Future Value and Present Value calculators handle both lump sums and payment streams; Future Value also splits the result into your contributions versus interest earned, so you can see where the balance came from.

Why CAGR is the honest way to annualize

If an investment goes up 50% one year and down 50% the next, the simple average return is 0% — but you have actually lost money. Start with $100, gain 50% to $150, lose 50% to $75. You are down 25%. This gap is why the arithmetic average of yearly returns overstates what you really earned.

• CAGR (compound annual growth rate) is the geometric average — the single steady rate that turns your start value into your end value. The formula is CAGR = (End/Start)^(1/years) − 1.
• The arithmetic mean simply adds the yearly returns and divides. It is always equal to or higher than CAGR, and the gap widens as returns get more volatile.
• CAGR is what you actually experienced; the arithmetic mean is a statistical average that ignores compounding order.
• Use CAGR to compare investments held for different lengths of time or with bumpy year-to-year results.

The Average Return calculator computes both and shows the difference explicitly, because mistaking one for the other is one of the most common investor errors.

ROI vs annualized ROI

Return on investment tells you the total percentage gain, but by itself it hides the clock.

• Total ROI is ROI = (gain − cost) / cost × 100%. It is simple and useful for a single, finished project.
• The trap: a 40% ROI sounds great until you learn it took ten years. That is only about 3.4% per year.
• Annualized ROI converts the total into a per-year rate — (1 + ROI)^(1/years) − 1 — so a quick flip and a long hold can be compared side by side.
• Always annualize when holding periods differ. Otherwise you will favor slow investments that simply had more time to accumulate.

The ROI calculator reports both figures so short and long holds compare fairly.

IRR, XIRR, and why they need iteration

When money goes in and out at several different times, a single ROI number is not enough. The internal rate of return (IRR) is the discount rate that makes the net present value of all those cash flows equal zero — effectively, the investment’s true compound return.

• There is no clean formula to solve for IRR directly. A calculator has to guess a rate, check whether NPV lands on zero, and adjust — repeating until it converges. This iteration is why IRR is a solver, not a plug-in equation.
• IRR assumes evenly spaced periods. Real cash flows rarely arrive on tidy anniversaries.
• XIRR is the version that accounts for the actual calendar dates of each cash flow, so irregular timing is handled correctly.
• NPV is the companion metric — plug in your own required rate and see whether the deal creates or destroys value at that hurdle.

The IRR calculator offers both standard IRR and XIRR, and shows NPV alongside. The Payback Period calculator answers the related, simpler question of how long until you recover your initial outlay, with a discounted option that respects the time value of money.

Fees compound too — quietly, against you

An expense ratio is the annual percentage a fund charges. It sounds tiny, but it compounds every year against your entire balance, and the drag grows as your balance grows.

Consider $100,000 invested for 30 years at a 7% gross return, with no further contributions:

• At a 0.03% expense ratio (a cheap index fund), you net roughly 6.97% and end near $754,000.
• At a 0.75% expense ratio (a pricier active fund), you net roughly 6.25% and end near $616,000.
• That 0.72% difference costs about $138,000 — money that left your account purely as fees and forgone compounding, not market losses.

That is the whole point of the ETF Fee Comparison calculator: a fee gap that looks like a rounding error becomes tens of thousands of dollars over a lifetime. The Mutual Fund calculator makes the same drag concrete by showing your future value gross versus net of fees, and totaling the dollars paid.

Dividends and reinvestment (DRIP)

Many stocks and funds pay dividends. What you do with them changes the outcome dramatically.

• Take the cash and your share count stays flat; you get income but less growth.
• Reinvest (a DRIP — dividend reinvestment plan) and each payment buys more shares, which then pay their own dividends. This is compounding applied to income.
• Over decades, reinvested dividends have historically made up a large share of total stock market returns.

The DRIP calculator contrasts reinvesting against pocketing the cash and charts how the share count itself grows over time.

Inflation and real returns

A return you can spend is a nominal return. What it actually buys is the real return.

• Real return ≈ nominal return − inflation. A 7% return during 3% inflation is only about 4% in purchasing power.
• Inflation is measured by the change in a price index (CPI): Adjusted = amount × (CPI_end / CPI_start), or you can assume a fixed annual rate for projections.
• Always sanity-check long plans in real terms. A big future number can be less impressive once you deflate it back to today’s dollars.

The Inflation calculator shows what a sum is worth across years using a dated, cited CPI dataset, plus a fixed-rate mode for forward projections.

Dollar-cost averaging vs lump sum

If you have money to invest, should you put it all in at once or spread it out?

• Lump sum means investing the full amount immediately. Because markets rise more often than they fall, this wins more often than not over long horizons.
• Dollar-cost averaging (DCA) means investing a fixed dollar amount on a schedule. You buy more shares when prices are low and fewer when high, so your average cost per share lands below the average market price over the period — and the ride is smoother.
• DCA’s real advantage is behavioral — it removes the pressure of timing and keeps you investing consistently, which is what most people can actually stick to.
• DCA is automatic when you contribute from each paycheck; you are already doing it inside a 401(k).

The DCA calculator compares dollar-cost averaging against a lump sum on the same price path and shows your blended cost basis.

The tools, in one place

Beyond the core solvers, BedrockCalc includes specialized calculators for particular assets: the Bond calculator prices a bond and solves for yield to maturity plus duration; the Options Profit calculator plots a single-leg payoff with break-even and max loss marked; and the Position Size calculator sizes a trade by the dollars you are willing to risk. Whatever the instrument, the discipline is the same — annualize honestly, account for fees and inflation, and compare on equal footing.