Savings Interest Rate Calculator

What this savings interest rate calculator does

Most savings tools ask what you have and tell you what you will end up with. This one runs the other way. You tell it what you have, what you want, and how long you have got, and it tells you the annual interest rate that would get you there.

Which is a more useful question than it first appears, because it turns a vague wish into a number you can go and check. "I would like 5,000 in three years" is a hope. "I need 7.72 percent a year" is something you can take to a rate comparison table and either find or not find.

Quite often you will not find it, and that is the tool doing its job. Better to learn it now than in three years.

Everything runs in your browser and nothing is stored.

How to use it

1. Interest Type. Simple or Compound. Compound is selected by default and is the right choice for nearly everyone. More on this below.
2. Initial Deposit. What you are starting with.
3. Years of Savings. Whole years.
4. Savings Goal. What you want at the end. It has to be larger than your deposit, otherwise no positive rate is needed and the tool will say so.

Press Calculate. Press Reset to clear it.

Worth being clear about the shape of what it is answering. This works out the rate needed for a single lump sum to grow into your goal on its own. It does not include monthly deposits. If you plan to keep adding money, and most people do, the rate you actually need will be a lot lower than what this returns, and our savings calculator handles contributions properly.

Solving the formula backwards

Ordinarily you know the rate and you are hunting for the final amount. Here you know the final amount and you are hunting for the rate, so the formula gets rearranged.

On the compound setting, the growth equation is goal = deposit × (1 + r)^years. Rearranged for r:

r = (goal ÷ deposit)^1/years − 1

On the simple setting, the equation is goal = deposit × (1 + r × years), which rearranges more easily:

r = (goal ÷ deposit − 1) ÷ years

Both come out as decimals and the tool multiplies by 100 to show you a percentage. The compound version assumes interest is added once a year. If your account compounds monthly, the rate you actually need is a shade lower than the figure shown, because more frequent compounding does some of the work for you.

The interest earned figure it reports is simply your goal minus your deposit, which is the gap the interest has to close.

A worked example: 4,000 into 5,000

You have 4,000. You want 5,000. You have three years. On the compound setting the tool returns 7.72 percent a year.

Where that comes from: 5,000 ÷ 4,000 = 1.25. The cube root of 1.25 is 1.0772. Subtract 1 and you have 0.0772, or 7.72 percent.

Check it forwards. 4,000 × 1.0772³ = 5,000. It closes exactly, which it should.

Now switch the dropdown to Simple and the answer becomes 8.33 percent. Higher, and for a reason worth understanding. Under simple interest your interest never earns interest of its own, so the rate has to work harder to cover the same ground. Compounding is doing part of the job for free.

Notice how small that gap is over three years, about six tenths of a percentage point. Stretch the same exercise out and it stops being small. Doubling 10,000 into 20,000 over ten years needs 7.18 percent compound, or 10 percent flat under simple interest. Nearly three points of difference, purely from letting interest sit on interest.

Which of the two settings you want

Compound, almost always. Nearly every savings account, deposit and investment on earth reinvests your interest, and compound is what that behaviour is called.

Simple is the right choice in a narrower set of cases. A non cumulative fixed deposit that pays your interest out to you each period rather than adding it to the balance. A bond that pays a coupon you spend rather than reinvest. A loan you made to somebody at an agreed flat rate. In all of those the principal genuinely never grows, so simple is the honest model.

If you are unsure, ask yourself one question: does the interest stay in the account? If yes, compound. If it gets paid out to you, simple.

And a small warning about direction. Compound always returns the lower required rate of the two. So if you pick the wrong setting you will not be dangerously wrong, you will just be aiming at a slightly harder or easier target than necessary. Over long horizons that gap gets wide, though, so it is worth getting right.

You have just calculated a CAGR

Something worth pointing out, because it makes this tool useful well beyond savings accounts.

The compound formula above is exactly the compound annual growth rate, or CAGR, which is the standard way analysts describe how fast anything has grown over a period. Same arithmetic, different job title.

So you can point this tool backwards at history rather than forwards at a goal. Put your starting value in the deposit field, the ending value in the goal field, and the number of years between them. What comes back is the annualised growth rate.

Revenue that went from 100,000 to 250,000 over twelve years grew at 7.93 percent a year. A fund that went from 4,000 to 5,000 in three years returned 7.72 percent annually. A house that doubled in nine years appreciated at 8.01 percent, which incidentally is why the rule of 72 tells you 72 divided by 8 is 9 years.

The reason CAGR matters is that it smooths out the lumps. A fund that went up 40 percent then down 20 percent then up 10 percent did not average 10 percent a year, it compounded to about 7.2. Averaging the yearly percentages overstates almost every real investment, and CAGR is the figure that tells the truth.

Is the rate you need actually out there?

The tool will happily return 34 percent a year if that is what your goal demands. It has no opinion about whether that is available. You should.

A rough guide to where the required number lands you. Anything at or below the going rate on ordinary savings accounts is comfortable, and you can go shopping for it. A few points above that and you are into fixed deposits, longer lock ups, and giving up access to your money for the term. Well into double digits and you are talking about market returns, which come with the real possibility of the number going down instead of up, and which are not something anybody can promise you over a fixed three year window.

Past twenty percent a year, guaranteed, the honest answer is that this does not exist and anyone offering it is selling you something else.

If the number that comes back is uncomfortable, you have three levers rather than one. Save more up front, so the deposit does more of the work. Give it more time, which is by far the most powerful of the three. Or adjust the goal. Adding regular monthly deposits is usually the easiest fix of all, and it is the one this particular tool cannot see.

Also remember the answer is a gross rate. Tax on interest and inflation both eat into it, so the real world rate you need is higher than the one displayed.

Questions people ask

Can I include monthly deposits?

Not in this tool. It solves for a single lump sum growing on its own. With regular contributions the rate you need drops considerably, and our savings calculator models those.

Is this the same as CAGR?

On the compound setting, yes, identical arithmetic. Put a past starting value and ending value in and you get the annualised growth rate for that period.

Which compounding frequency does it assume?

Annual. If your account compounds monthly or quarterly, the nominal rate you need is slightly lower than the figure shown.

Why does it refuse a goal smaller than my deposit?

Because you would need a negative interest rate to get there, which is not what anybody is asking when they set a savings goal. It stops and tells you rather than returning a confusing minus sign.

Can I use a period shorter than a year?

Not directly, the years field wants whole numbers from 1 up. For shorter horizons, work the compound formula by hand with years as a fraction.

The rate it gave me looks impossible. What now?

It probably is. Extend the timeline, raise the starting deposit, lower the goal, or start adding to it monthly. Time is the cheapest of those four.

References

A note on sourcing. The compound growth equation and its rearrangement to solve for a rate are standard time value of money results. The distinction between an advertised annual percentage yield and a nominal rate, which determines whether the figure returned here matches what a bank quotes you, is defined in Regulation DD.

1. OpenStax, Principles of Finance, Section 7.2, Time Value of Money Basics. https://openstax.org/books/principles-finance/pages/7-2-time-value-of-money-tvm-basics
2. Consumer Financial Protection Bureau, Appendix A to Part 1030, Annual Percentage Yield Calculation. https://www.consumerfinance.gov/rules-policy/regulations/1030/A
3. Kellison, S. G., The Theory of Interest, 3rd edition, McGraw-Hill, 2008.
4. U.S. Securities and Exchange Commission, Office of Investor Education and Advocacy, Compound Interest Calculator. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator