Maturity Value Calculator

What a deposit matures into

Maturity value is the plainest question in savings. You put an amount away for a fixed stretch at a fixed rate. How much comes back at the end?

Three inputs, one answer. The amount, the rate, and how long, with a dropdown so you can express the time in whatever unit the offer was written in.

It suits fixed deposits, term deposits, bonds held to maturity, recurring arrangements with a single lump payment at the end, and any other case where money goes in once and comes back once.

The arithmetic is compound growth, which is not complicated. What is worth knowing is the compounding convention it uses, because for anything shorter than a year the convention matters more than you would expect and different institutions use different ones.

Three fields and a unit

1. Principal. The amount you are depositing.
2. Interest rate. The annual rate, as a percentage.
3. Time of investment. How long, with a dropdown for days, weeks, months or years.

Press Calculate and you get the maturity value.

The result is the total coming back, principal and interest together. If you want the interest on its own, subtract your principal from it. On a deposit of 1,00,000 that matures at 1,40,255, the interest was 40,255.

The dropdown exists because deposit offers are written in whatever unit suits the seller. Ninety days, six months, one year, twenty six weeks. Enter it as written rather than converting in your head, since the conversion is where mistakes happen.

Annual compounding, including part years

One formula:

Maturity value = P × (1 + r)^t

P is the principal, r is the annual rate as a decimal, and t is the time expressed in years. The dropdown's job is to turn whatever you typed into years before the exponent is applied. Six months becomes 0.5, ninety days becomes about 0.2464, and so on.

So the compounding here is annual, and for periods that are not whole years the annual rate is applied to a fractional exponent.

That is worth stating clearly because it is a genuine choice among several. It treats your quoted rate as an effective annual rate and works out what fraction of that year's growth applies. A half year gets the square root of the annual growth factor, not half of it.

For whole years this matches what everybody expects. For part years it produces a slightly lower figure than the two other common conventions, and the next section shows by how much.

A lakh at seven percent

Principal 1,00,000, rate 7 percent.

Look at the one year row against the five year row. Five times the duration produces just under six times the interest, because each year's growth builds on the last.

Then look at the six month row. The interest is 3,441 rather than 3,500, which is what you would get by halving the annual 7,000. Slightly less than half a year's interest for half a year, and the reason is the convention described above. A half year earns the square root of the annual growth, and the square root of 1.07 is 1.0344 rather than 1.035.

Three ways to price six months, and they disagree

Here is the part worth understanding before you compare this figure against a bank's own quote.

Take that same 1,00,000 at 7 percent for six months. Three conventions are in common use and all three are legitimate.

A spread of 110 across the three, on a deposit of a lakh for half a year. Small in absolute terms, and it scales with both the amount and the rate.

Which one your bank uses depends on the product and the market. Short term deposits are frequently priced on simple interest, since nothing has compounded yet. Indian fixed deposits commonly compound quarterly. Some instruments use the fractional method this tool uses. The rate on the page is the same in every case, and the money at the end is not.

So the honest way to use this: for whole year periods, the answer here will match almost any bank. For part years, treat it as a close estimate and take the exact figure from the deposit receipt, which will state the maturity amount explicitly.

And when you are comparing two offers, make sure both are quoted on the same basis. If one advertises an effective annual yield and the other a nominal rate compounded quarterly, they are not comparable as written. The nominal interest rate calculator converts between the two.

Days, weeks, months, years

All four options do the same thing, which is to convert your number into years before the exponent is applied.

• Years divides by 1.
• Months divides by 12.
• Weeks divides by 52.18.
• Days divides by 365.25.

Those last two carry a detail worth knowing. The day count uses 365.25 rather than 365, which is the average length of a year once leap years are counted. It is the astronomically tidy choice and it produces a small quirk: entering 365 days gives 0.999316 years rather than exactly 1.

On our lakh at 7 percent, that is 1,06,995 instead of 1,07,000. Five rupees on a lakh.

Nothing to worry about, and there is a simple habit that avoids it entirely. Enter the period in the largest unit that fits. One year rather than 365 days. Six months rather than 182 days. Two years rather than 24 months. Each conversion introduces a rounding, and the fewer you use the cleaner the answer.

Where days genuinely help is for the odd periods deposits actually come in. Ninety days, forty five days, a term running to a specific date. For those, days is the right unit and the small imprecision is well inside the difference between conventions discussed above.

Checking what a bank is offering you

The most useful thing to do with this is not to project, but to verify.

When a deposit is offered, you are usually told two things: a rate and a maturity amount. Run the rate and the term through here and compare against the amount they quoted.

If the two land close, the offer is what it appears to be. If the quoted maturity is meaningfully below what this returns, ask why, since the usual explanations are a different compounding convention, a fee, or tax deducted at source. If it is meaningfully above, ask too, since the rate you were told may not be the rate being applied.

Two other things to raise while you have someone's attention.

What happens if you break the deposit early. Most fixed deposits pay a reduced rate on premature withdrawal, and some charge a penalty on top. The maturity value assumes you go the distance.

Whether interest is paid out or accumulated. This calculation assumes it stays in and compounds. A deposit that pays interest to your account each quarter returns the same interest in total but does not compound, so the maturity figure will be lower and you will have had the money earlier.

One last thing that sits outside the arithmetic: interest on deposits is generally taxable, and in several countries tax is deducted at source before the money reaches you. The figure here is before tax.

This is an estimate for comparison and planning, not a quote, and nothing here is financial advice.

Questions people ask

What is maturity value?

The total amount returned at the end of a deposit or investment, principal and interest together. Subtract your principal from it to see the interest alone.

How is it calculated?

Principal multiplied by one plus the annual rate, raised to the power of the time expressed in years. On 1,00,000 at 7 percent for 5 years that gives 1,40,255.

How often does it compound?

Annually. For periods that are not whole years, the annual rate is applied to a fractional exponent, so six months earns the square root of a full year's growth.

Why is six months not half a year's interest?

Because compounding is not linear. At 7 percent, a full year adds 7,000 on a lakh and six months adds 3,441 rather than 3,500. The half year earns the square root of the annual growth factor.

Why does my bank quote a different maturity amount?

Most likely a different compounding convention. Short deposits are often priced on simple interest, and Indian fixed deposits commonly compound quarterly. On a six month deposit of a lakh at 7 percent the three common methods differ by about 110.

Should I enter days or years?

Use the largest unit that fits your term. One year rather than 365 days, since each conversion introduces a small rounding. Days are the right choice for odd terms like 90 or 45 days.

Why does 365 days not equal one year?

The day conversion uses 365.25, the average year length once leap years are counted, so 365 days works out as 0.999316 years. The effect is about five rupees on a lakh at 7 percent.

Is the figure after tax?

No. Deposit interest is generally taxable, and in several countries tax is deducted at source before the money reaches you, so expect to receive less than the figure shown.

What if the interest is paid out rather than accumulated?

Then it does not compound, and the total returned will be lower than this figure. The calculation assumes interest stays in the deposit and earns alongside the principal.

References

The maturity value uses the standard compound accumulation relation, under which a present amount grows to a future value at a periodic rate applied over a number of periods, as set out in university financial mathematics materials for the actuarial syllabus. The distinction between an effective annual rate, which reflects compounding across a year, and a nominal annual rate expressed as a periodic rate multiplied by the number of periods in a year, follows Regulation DD and Regulation Z respectively. That distinction is what separates the three conventions compared above for periods shorter than a year.

1. J. Robert Buchanan, Millersville University, Loan Repayment, MATH 372 Financial Mathematics I. https://sites.millersville.edu/rbuchanan/math372/LoanRepayment-handout.pdf
2. Miguel A. Arcones, Binghamton University, Manual for SOA Exam FM, Chapter 4: Amortization and Sinking Funds. https://people.math.binghamton.edu/arcones/exam-fm/sect-4-1.pdf
3. Consumer Financial Protection Bureau (CFPB), 12 CFR Part 1030, Truth in Savings (Regulation DD), and Appendix A: Annual Percentage Yield Calculation. https://www.ecfr.gov/current/title-12/chapter-X/part-1030
4. Consumer Financial Protection Bureau (CFPB), Regulation Z, Appendix J to Part 1026: Annual Percentage Rate Computations for Closed-End Credit Transactions. https://www.consumerfinance.gov/rules-policy/regulations/1026/j/