Compound Interest Guide

How to Choose an Interest Rate Assumption

Written by Mimai for Compound Growth Calculator · Educational guide

Open any compound interest calculator and you will face the same question: what rate should I type in? It looks like a trivial choice, a single number among several inputs. It is not. The rate is the lever that moves the whole projection, and a difference of one percentage point can quietly change a twenty-year plan by thousands of dollars. This guide is about how to pick that number honestly — and how to keep it from flattering your expectations.

One box, outsized influence

In the compound interest formula A = P(1 + r/n)^nt, the rate r appears inside a power. Powers amplify everything around them: small changes in r produce outsized changes in A as the time horizon lengthens. Your starting amount matters, your contributions matter, and the number of years matters — but the rate multiplies the effect of all three. That is why a projection built on an optimistic guess and one built on a realistic guess can both be "correct" by their own assumptions and still tell completely different stories.

The uncomfortable implication is that a calculator output is only as honest as its inputs. Run the same plan at 4% and 8% and you have two plausible-looking futures that differ by multiples. Neither number is wrong; the assumptions are just different. So the first skill is not arithmetic — it is humility about the input.

Two kinds of rates, two very different jobs

Before choosing a number, decide which kind of rate your scenario calls for. The two most common categories are easy to confuse, and they serve opposite purposes.

Deposit rates apply when the money sits in a savings account, money-market account, or certificate of deposit. These rates are close to what banks actually pay, are usually predictable for a year or two, and — importantly — are typically the lowest rates in personal finance. If you are modeling an emergency fund or a near-term savings goal, the rate you enter should look like a deposit rate. Anything higher would be fiction. Rates in this category have moved up and down with central-bank policy in recent years; a reasonable placeholder might be in the low single digits, and the exact number is easy to verify by checking current offerings.

Long-term investment returns apply when the money is in a broadly diversified stock index fund or similar investment. These are not promised or guaranteed; they are historical averages with wide year-to-year swings. Commonly cited long-run averages for broad stock indexes fall somewhere in the mid-single digits to low double digits before inflation, but individual decades have ranged far above and below that. No one can promise a future average, which is precisely why the number you choose should be treated as a scenario, not a forecast.

The two categories should never be swapped. Putting a stock-market-style rate on a savings-account projection makes the plan dishonest in a flattering direction. Putting a deposit rate on a decades-long investment projection makes it unrealistically timid. Decide what the money will actually sit in, then pick the matching category.

Conservative, neutral, optimistic: three example assumptions

A useful habit is to run every plan three times rather than once. Pick a conservative case, a neutral case, and an optimistic case, and treat the band between them as the honest range of outcomes. Here is one example set for a goal twenty years out, saving $100 per month — the numbers are placeholders, not recommendations, and your own tiers should reflect the actual products you plan to use.

Notice what the table does not show: $24,000 of your own contributions appear in every row. The difference between the rows is purely what the assumed rate added on top — $7,097 in the conservative case versus $34,902 in the optimistic one. Presenting plans this way keeps the contribution column honest and makes the rate assumption visible, rather than hidden inside a single magic number.

Worked example: why one extra percent changes everything

Let's isolate the rate by holding everything else fixed. Take a one-time deposit of $10,000, no further contributions, a 20-year horizon, and three rates: 4%, 5%, and 6%. Compounding annually:

• At 4%: $10,000 × 1.04²⁰ = $21,911.23
• At 5%: $10,000 × 1.05²⁰ = $26,532.98
• At 6%: $10,000 × 1.06²⁰ = $32,071.35

Each extra percentage point added roughly $4,600 to $5,500 to the final balance — on a starting amount of $10,000. The gap between the 4% and 6% scenarios, $10,160, is larger than the entire initial deposit. This is compounding's signature: the rate does not add a flat amount; it acts on everything that has accumulated so far, so its influence grows with each passing year. A plan that looks "almost the same" at year one is a completely different plan by year twenty.

There is a good sanity check buried in this example. If a projection tells you your $10,000 becomes $80,000 in twenty years, the implied rate is roughly 11% — possible in a favorable stock-market decade, but far beyond any deposit product. Checking the implied rate behind an exciting number is the fastest way to catch an assumption that has drifted out of reality. The mechanics of the underlying formula are explained step by step in the compound interest formula guide.

A one-minute sensitivity check you can run yourself

You do not need special tools to see how fragile a projection is. Take any plan and rerun it with the rate moved by exactly one percentage point in each direction. Compare the three results. If the spread is a rounding error, your rate barely matters and you can stop worrying. If the spread is the size of a car, a house, or a retirement — then the rate is doing the work, and the rest of the plan is detail.

Here is the quick version with a $5,000 lump sum over 10 years, a timeframe short enough that the differences are still modest:

• 3%: $6,719.58
• 5%: $8,144.47
• 7%: $9,835.76

Already the 7% case ends more than $3,100 ahead of the 3% case. Extend the same three rates to twenty or thirty years and the spread stops being a footnote. The habit to build is running the same plan across a range rather than once with your favorite number — the range, not any single point, is the useful output of a calculator. And when you settle on a rate for a deposit product specifically, remember that the bank's quoted APY is already the right input, as covered in the APY vs interest rate guide.

A checklist for picking your number

• Name the vehicle first. Savings account, CD, index fund, or bond? The vehicle dictates the rate category. If you are unsure, read what compound interest is and start with the safest assumption.
• Use the advertised rate for deposits. For savings accounts and CDs, the APY on the bank's disclosure page is a fact, not a guess. Enter it and move on.
• Use a modest long-term average for investments. For diversified stock investments, choose a number from the commonly cited historical ranges, subtract something for fees and taxes, and label it a scenario.
• Run three tiers. Conservative, neutral, and optimistic. Plan around the conservative end for survival; dream with the optimistic end only after the conservative math works.
• Check the implied rate of any exciting output. If a result seems too good, solve for the rate and see whether it matches reality.
• Review the assumption yearly. Deposit rates change, plans change, and a rate picked at age 25 is rarely right at age 35.

Choosing a rate assumption is ultimately an exercise in honesty. The calculator will faithfully multiply whatever you feed it — it cannot tell the difference between a rate pulled from a bank's website and one pulled from optimism. Feeding it a defensible number, and testing that number against its neighbors, is the entire job.