Savings Calculator
Compound savings with monthly deposits, printed in money and in what the money will buy, with each deposit discounted from the month it was actually made.
Starting balance $5,000.00
Monthly deposit $400.00, at the end of each month
Rate 4.5% a year, compounded monthly
Term 10.0 years, 120 months
In money
balance at the end $68,314.19
paid in $53,000.00
interest $15,314.19, 22.4% of the balance
In today's money
balance is worth $51,829.83 at 2.8% inflation
inflation takes $16,484.36
what you paid in is worth $46,894.30, each deposit discounted from the month it was made
real gain $4,935.53
real rate 1.65% a year, which is the rate over inflation rather than the difference between them
reading the savings keep ahead of inflation, though by much less than the headline interest suggests
Against the goal
goal $75,000.00
reached in 131 months, 10.9 years
against your term 0.9 years short
the goal in today's money $56,902.34, which is what it will buy
deposit that would get there $450.46 a month
When the money does its work
the first 1 year $15,176.35 of the final balance, 22.2% of it
the first 3 years $28,905.95 of the final balance, 42.3% of it
the first 5 years $41,455.97 of the final balance, 60.7% of it
If the rate were different
at 1% $55,985.57
at 3% $62,643.34
at 5% $70,347.96
at 7% $79,282.23
The balance is $68,314.19 and it buys what $51,829.83 buys today.
Against $46,894.30 of purchasing power paid in, the real gain is
$4,935.53, which is what the account earned after inflation took its
share of both.
The real rate is the rate over inflation rather than the rate minus
inflation: 1.65% rather than 1.7%. The difference is small at these
levels and it grows quickly at high ones.
Deposits early in the term do most of the compounding, because they have
the whole term to do it in. That is the arithmetic behind starting
sooner beating saving harder: the same money paid in five years earlier
is worth meaningfully more at the end.
The rate on a savings account is not fixed, and it does not follow the
central bank rate upwards as promptly as it follows it down.
Introductory rates in particular revert, which is why the honest version
of this calculation uses the rate you will have rather than the rate you
were offered.
Tax is not in these figures. Interest is usually taxable, so the real
return is lower again unless the money sits in a sheltered account, and
the difference between a taxed and a sheltered account over a long term
is larger than the difference between two rates.
This is arithmetic, not advice. For a goal several years away, savings
accounts trade return for certainty; for one several decades away, the
certainty is what costs the most. Which trade is right depends on facts
about you that no calculator has.
The projection assumes the deposit never changes and is never missed.
Real saving is interrupted, and a plan that only works if nothing goes
wrong is a plan with one assumption too many.
Output is valid and updates as you type.
Fix the highlighted fields to update the output.
A savings calculator that stops at the nominal balance answers the easy half of the question. $68,314 in ten years is not $68,314: at 2.8 percent inflation it buys what about $51,830 buys today, and the gap is larger than the interest earned.
So everything here is printed twice. The comparison that matters is the real value of the balance against the real value of what was paid in, with each deposit discounted from the month it was actually made. A deposit in year nine gives up less purchasing power than one in year one, and deflating the whole balance while leaving the contributions at face value is the usual way this gets got wrong.
The other thing worth seeing is when the money does its work. On the example, the first five years’ deposits account for 60.7 percent of the final balance, because they had the whole term to compound in. That is the arithmetic behind starting earlier beating saving harder.
How to use
- Put in the starting balance, the monthly deposit, the rate and the term.
- Put in an inflation rate to see the whole thing in today’s money.
- Add a goal to get the month it is reached, and the deposit that would reach it inside your term.
Example
$5,000 to start, $400 a month at 4.5 percent for ten years, with 2.8 percent inflation and a $75,000 goal:
In money
balance at the end $68,314.19
paid in $53,000.00
interest $15,314.19, 22.4% of the balance
In today's money
balance is worth $51,829.83 at 2.8% inflation
inflation takes $16,484.36
what you paid in is worth $46,894.30, each deposit discounted from the month it was made
real gain $4,935.53
real rate 1.65% a year, which is the rate over inflation rather than the difference between them
Against the goal
reached in 131 months, 10.9 years
against your term 0.9 years short
the goal in today's money $56,902.34, which is what it will buy
deposit that would get there $450.46 a month
When the money does its work
the first 1 year $15,176.35 of the final balance, 22.2% of it
the first 5 years $41,455.97 of the final balance, 60.7% of it
If the rate were different
at 3% $62,643.34
at 7% $79,282.23Ten years of saving turns $46,894 of purchasing power into $51,830 of purchasing power. That is the real answer, and it is a long way from $15,314 of interest.
Pitfalls
A nominal balance is not a result. Always read it next to the real one. Over a long term inflation takes more than the interest adds at any ordinary savings rate.
The real rate is a ratio, not a subtraction. 4.5 percent against 2.8 percent inflation is 1.65 percent, not 1.7. The difference is small at these levels and grows quickly at high ones.
Compare like with like. Deflating the balance and comparing it against nominal contributions overstates the loss. Each deposit has to be discounted from its own month, which is what the contributions line does.
Early deposits do most of the compounding. The same money five years earlier is worth meaningfully more at the end, which is why the answer to “should I wait until I can afford more” is usually no.
Introductory rates revert. Use the rate you will have for most of the term rather than the one on the advert, or split the calculation at the point it changes.
Tax is not in these figures. Interest is usually taxable, and the difference between a taxed and a sheltered account over a long term is larger than the difference between two rates.
A plan with no missed deposits is one assumption short. Real saving is interrupted. Check what the goal looks like at a lower deposit before committing to the higher one.
Compatibility
Arithmetic in the browser: nothing is uploaded and nothing is stored.
The rate is compounded monthly and the deposit defaults to the end of the month, which is the convention most savings accounts follow. The start-of-month option multiplies the stream by one plus the monthly rate, which the test suite asserts exactly, so the two options differ by precisely one month of growth rather than by an approximation.
A zero rate is handled without dividing by it, so the balance is simply the contributions. The goal search walks month by month up to a hundred years and reports that a goal is out of reach rather than returning a misleading figure, and the required deposit is found by stepping upwards until the term covers the goal.
Real contributions are computed by discounting each monthly deposit at the monthly equivalent of the annual inflation rate, which is the twelfth root of it rather than a twelfth of it.