Maturity Value Calculator
What a deposit matures at, with the effective annual rate beside the quoted one, every compounding frequency compared, and tax and inflation applied.
Deposit $25,000.00
Nominal rate 5% a year
Compounded monthly, 12 times a year
Term 10.00 years
Maturity value $41,175.24
interest earned $16,175.24
as a multiple 1.6470×
Effective annual rate 5.1162%
the quoted rate 5%
the difference 0.1162%, which is what compounding adds
Against simple interest
simple interest value $37,500.00
compounding adds $3,675.24
as a share of the interest 22.7%
At every frequency
annually $40,722.37 · 5% effective
half-yearly $40,965.41 · 5.0625% effective
quarterly $41,090.49 · 5.0945% effective
monthly $41,175.24 · 5.1162% effective ← yours
weekly $41,208.13 · 5.1246% effective
daily $41,216.62 · 5.1267% effective
continuous $41,218.03 · 5.1271% effective
What you keep
after 20% tax on the interest $37,940.19
in today's money at 3% $28,231.06
real gain $3,231.06
Doubling time at this rate 13.9 years
the rule of 72 says 14.4 years
A nominal 5% compounded monthly is an effective 5.1162%. The quoted rate
is the nominal one and the effective one is what you receive, which is
why two products can advertise the same rate and pay differently, and
why a comparison has to use the effective figure. That is what APY
means.
Compounding adds $3,675.24 over simple interest here, which is 22.7% of
the total interest. The share grows with the term: over a long deposit
most of the interest is interest on interest, which is the whole
argument for a long horizon.
Continuous compounding is the limit, not a product. It is the ceiling on
what more frequent compounding can do, and the gap between daily and
continuous is tiny, which is why nobody sells it and why arguing about
daily against monthly is worth less than half a point of rate.
In today's money the maturity value is worth $28,231.06. That is the
number to plan with, since a deposit that grows slower than prices loses
value while appearing to gain it.
Tax is applied to the interest rather than the whole balance, which is
the usual treatment for a deposit. Where the tax is withheld each period
rather than at maturity, the compounding base is smaller and the outcome
slightly worse than this.
The rule of 72 approximates the doubling time and drifts at high rates.
The exact figure comes from logarithms and is printed above; the rule is
accurate to within a few months around 8 percent.
A fixed-term deposit usually cannot be broken without losing interest,
and the rate is fixed while rates are not. A higher rate for five years
is a bet that rates will not rise, which is a different decision from
the arithmetic here.
Output is valid and updates as you type.
Fix the highlighted fields to update the output.
Five percent compounded monthly is not five percent. It is 5.1162 percent, and that figure, the effective annual rate, is the one you actually receive and the only one two products can be compared on.
The rate on the poster is the nominal rate. Add the compounding frequency and you get the effective rate, which is what APY means. The difference is small on one year and substantial over ten: the same $25,000 at a nominal 5 percent matures at $40,722 compounded annually and $41,175 compounded monthly.
The other thing worth seeing is how much of the interest is interest on interest. Over ten years it is nearly a quarter, which is why a simple-interest calculation understates a long deposit badly.
How to use
- Put in the deposit, the quoted annual rate and the term.
- Set the compounding frequency. It is the input people leave out and it changes the answer.
- Add tax on the interest and an inflation rate to see what you keep.
Example
$25,000 at a nominal 5 percent for ten years, compounded monthly:
Maturity value $41,175.24
interest earned $16,175.24
Effective annual rate 5.1162%
the quoted rate 5%
the difference 0.1162%, which is what compounding adds
Against simple interest
simple interest value $37,500.00
compounding adds $3,675.24
as a share of the interest 22.7%
At every frequency
annually $40,722.37 · 5% effective
quarterly $41,090.49 · 5.0945% effective
monthly $41,175.24 · 5.1162% effective ← yours
daily $41,216.62 · 5.1267% effective
continuous $41,218.03 · 5.1271% effective
What you keep
after 20% tax on the interest $37,940.19
in today's money at 3% $28,231.06
real gain $3,231.06The gap between monthly and daily compounding is $41. The gap between 5 percent and 5.5 percent is about $2,100. Rate beats frequency, comfortably.
Pitfalls
A rate without a frequency is incomplete. Two accounts advertising 5 percent can pay differently, and the comparison has to be on the effective rate. In the United States that is what APY means and it is required on advertising; elsewhere the label varies.
APR and APY are not the same. APR is the nominal rate, often with fees folded in for lending; APY is the effective rate including compounding. A savings product quoting APR and a competitor quoting APY are not being compared.
Continuous compounding is a limit, not a product. It is the ceiling on what frequency can achieve, and the gap between daily and continuous is negligible. Arguing about monthly against daily is worth less than half a point of rate.
Tax withheld each period compounds less. Where the interest is taxed as it is credited rather than at maturity, the base that compounds is smaller and the outcome slightly worse than shown here.
A deposit below inflation loses value while the balance rises. That is the normal state of a savings account in an inflationary period, and it is why the real figure is worth looking at rather than the nominal one.
A fixed term is a bet on rates. A higher rate for five years is only better if rates do not rise, and breaking most fixed deposits early costs the interest. The arithmetic here says nothing about that decision.
The rule of 72 drifts. It is accurate to within a few months around 8 percent and overstates at high rates. The exact doubling time is printed above.
Compatibility
Arithmetic in the browser: nothing is uploaded and nothing is stored.
The compound formula is P(1 + r/n)^(nt), with continuous compounding as Pe^(rt), which is the limit as
n grows. The effective rate is (1 + r/n)^n − 1, and the test suite pins the published figures: 5 percent
nominal is 5.1162 percent effective monthly and 5.1267 percent daily.
Tax is applied to the interest rather than the whole balance, at maturity, which is the simpler and more
common treatment. Inflation divides the after-tax value by (1 + i)^t, giving purchasing power in today’s
terms.
Every frequency is shown against the same deposit, so the comparison is arithmetic rather than assertion, and the tests check that the effective rate rises monotonically with frequency.