Finance
Savings Comparison
Savings Comparison applies the time value of money: a dollar today can grow, so future amounts are worth less in today's terms.
What this does
Savings Comparison applies the time value of money: a dollar today can grow, so future amounts are worth less in today's terms.
Investing calculators all answer one question in different forms: what does money become over time? Savings Comparison takes a starting amount, a rate of return, and a time horizon, then projects the future value. The engine underneath is compounding, the process where each period's growth is calculated on a balance that already includes all previous growth, so money accelerates the longer it stays invested.
The formula, explained plainly
The core formula is future value = P x (1 + r)^n, where P is the starting amount, r is the rate per period, and n is the number of periods. At 8% compounded yearly, $10,000 becomes about $21,589 after 10 years, but about $100,627 after 30 years, because the exponent does the heavy lifting. Small differences in r or n produce enormous differences in outcomes, which is why starting early usually beats saving more later.
CAGR, the compound annual growth rate, answers a different question: what steady yearly rate would turn the starting value into the ending value? It is calculated as (end/start)^(1/years) - 1. CAGR smooths a bumpy ride into one tidy number, which makes investments comparable, but it also hides volatility: two investments with the same CAGR can have felt completely different to live through.
NPV and IRR bring in the time value of money, the idea that a dollar today is worth more than a dollar next year because today's dollar can be invested. NPV discounts every future cash flow back to today's dollars at a chosen discount rate and subtracts the initial cost; a positive NPV means the project beats the discount rate. IRR is the discount rate that makes NPV exactly zero, so it reads as the project's built-in percentage return and can be compared against your required return.
Regular investing, called SIP in some countries and dollar-cost averaging in the US, changes the math from one lump sum to a stream of contributions, each compounding for a different length of time. Savings Comparison sums the future value of every contribution separately, which shows why consistency matters more than timing: missing the market's best days hurts far less than missing years of contributions. Bonds add a final twist, because a bond's price moves opposite to interest rates, so its quoted yield only holds if conditions cooperate.
How to use it
- Enter deposit.
- Enter account a rate (%).
- Enter account b rate (%).
- Enter years.
- Read the instant result and the breakdown below it.
- Adjust any input to compare scenarios.
Worked example
With deposit = 10000, account a rate (%) = 4.5, account b rate (%) = 5, years = 5, the result is $301.00 difference Account A (4.5%) is $12,461.82. Account B (5%) is $12,762.82. Extra interest with B is $301.00.. The defaults illustrate how steady compounding turns a modest start into a much larger sum.
Common mistakes
- Forgetting taxes on the gains. Dividends, interest, and realized capital gains are all taxed, and a pre-tax projection can overstate what you keep by 15% to 30% or more.
- Assuming past returns predict future returns. Backtests describe what happened under conditions that will not repeat exactly; forward projections should use conservative rates.
- Comparing IRRs of projects with very different sizes or timing. IRR assumes interim cash flows reinvest at the IRR itself, which flatters projects with early payouts and can misrank mutually exclusive choices.
- Ignoring compounding frequency when comparing rates. A nominal 8% compounded monthly beats 8% compounded yearly, which is why APY (which reflects compounding) is the fair comparison, not the nominal rate.
- Treating a bond's yield as a guaranteed total return. If rates rise after you buy, the bond's market price falls, and selling early can mean a loss despite the quoted yield.
- Projecting retirement needs in today's dollars without inflation. A $1M target 30 years out at 3% inflation buys what about $412,000 buys today, so nominal targets mislead.
- Doing long-horizon math with simple interest intuition. People consistently underestimate compounding; money at 8% doubles roughly every 9 years, which linear thinking never predicts.
- Mixing nominal and real returns. A 7% return with 3% inflation is roughly a 4% real return, and it is the real return that determines what your money will actually buy.
Limitations
- IRR can produce multiple answers (or none) when cash flows alternate between positive and negative, making it unreliable for such projects.
- NPV is only as good as the discount rate you choose; a rate that is too low makes mediocre projects look attractive and vice versa.
- The math does not model sequence-of-returns risk: two retirees with identical average returns can have very different outcomes if a crash hits early versus late in withdrawals.
- Bond calculations assume the issuer pays on time and in full; default risk and call provisions are not modeled.
- Projections assume a constant rate of return, but real markets swing year to year; actual paths will wobble around any smooth curve shown here.
Expected accuracy
The formulas themselves are exact: given the inputs, compound growth, CAGR, NPV, and IRR are computed to full precision and will match a spreadsheet or financial calculator. The uncertainty lives entirely in the inputs, because future returns, inflation, and discount rates are guesses; treat every projection as a scenario to stress-test, not a promise.
Privacy
Everything you type stays on your device. The calculation runs in your browser with JavaScript; no input is sent to a server, stored in an account, or shared with anyone.
Sources and standards
- Calculations use the standard time-value-of-money formulas (future/present value, CAGR, NPV, IRR) as taught in corporate finance and implemented in spreadsheet functions like FV, XNPV, and XIRR; SIP math follows the future value of an annuity.
Bottom line
Savings Comparison shows what time and compounding do to money, which makes it a planning tool, not a crystal ball. Run it with a conservative return, then run it again with a pessimistic one, and build your plan around the worse outcome.
Key insight
Time beats timing. Starting ten years earlier matters more than earning an extra percent, because compounding multiplies every year you give it. The most powerful input is the one nobody wants to hear: start now.
Frequently asked questions
What is the difference between APY and interest rate?
The interest rate (nominal) is the stated rate before compounding frequency is considered; APY reflects the effect of compounding and is the true yearly growth. A 5% rate compounded monthly is about 5.12% APY. Always compare accounts and CDs using APY so compounding differences do not distort the comparison.
How are bond prices and interest rates related?
They move in opposite directions: when market rates rise, existing bonds paying lower coupons become less attractive, so their prices fall until their yield matches the market. A bond held to maturity still pays its promised coupons and principal, but selling early after a rate rise means accepting the lower price.
Should I worry about sequence-of-returns risk?
Yes, once you start withdrawing. Two portfolios with identical average returns end very differently if a crash hits in the first years of retirement versus the last, because early withdrawals lock in losses on a shrinking base. Mitigations include holding a cash buffer, flexible spending, and not retiring on the most optimistic return assumption.
Are dividends better than capital gains?
A dollar of total return is a dollar regardless of whether it arrives as a dividend or price appreciation, but taxes and control differ. Dividends are taxed in the year paid and you cannot defer them, while unrealized gains compound tax-deferred until you sell. Chasing high yield alone often means accepting slower growth or higher risk.
How much should I assume for future stock returns?
US stocks have returned roughly 10% nominal (about 7% real) over the very long run, but forward-looking planners often use 6% to 8% nominal to stay conservative. Using a modest assumption and saving a bit more is far safer than banking on the historical average and falling short. Always run a pessimistic scenario too.
What is dollar-cost averaging and does it beat lump sum?
Dollar-cost averaging invests fixed amounts on a schedule, buying more shares when prices are low and fewer when high. Studies show lump sums win about two-thirds of the time because markets rise more often than they fall. Averaging is still valuable behaviorally: it gets hesitant investors into the market and smooths regret.
Why do two calculators give slightly different results?
Common causes are compounding frequency (monthly versus yearly), whether contributions are assumed at the start or end of each period, and rounding of the rate. A monthly-contribution model and an annual-contribution model for the same SIP can differ by nearly a full year's growth on the contributions. Check the timing assumption before comparing outputs.
How does compound interest actually work?
Each period, growth is calculated on the current balance, which already includes all previous growth. At 8% yearly, $10,000 earns $800 in year one, but in year ten it earns about $1,599 because the balance has grown. This growth-on-growth effect is small at first and enormous over decades, which is why time matters more than the starting amount.
What is CAGR and when should I use it?
CAGR is the steady annual rate that would turn a starting value into an ending value over a given period: (end/start)^(1/years) - 1. Use it to compare investments over multi-year periods on equal footing. Just remember it smooths away volatility, so pair it with a look at the actual yearly ups and downs before judging risk.
What is the difference between nominal and real return?
Nominal return is the raw percentage gain; real return subtracts inflation to show growth in purchasing power. If your portfolio gains 7% while prices rise 3%, your real return is roughly 4%. For goals more than a few years out, like retirement, always think in real terms or you will overestimate what the money buys.
How do NPV and IRR differ?
NPV converts all cash flows to today's dollars at your chosen discount rate and subtracts the cost; positive means the project clears your hurdle. IRR is the discount rate that would make NPV zero, expressed as a percentage return you compare against your required rate. Use NPV for absolute value and IRR for a quick return-versus-hurdle check, and prefer NPV when they disagree.
What discount rate should I use for NPV?
Use your opportunity cost of capital: what you could earn on an alternative investment of similar risk, often 8% to 12% for business projects. A higher rate penalizes distant cash flows more heavily. If you are unsure, run the NPV at two or three rates and see whether the decision changes.
What is a SIP and how is it different from a lump sum?
A SIP (systematic investment plan) invests a fixed amount regularly, such as $500 a month, while a lump sum invests everything at once. Lump sums usually win when markets rise, because more money compounds longer, but SIPs remove timing stress and suit people investing from salary. The calculator sums each contribution's individual compounding to show the total.