How sinking fund deposits work
By Jude Wallis
A sinking fund works backwards from a known target to the deposit that reaches it. Saving $10,000 over five years at 6 percent needs $1,773.96 a year, because the early deposits earn interest for the years that follow them.
Deposit per period
$1,773.96
Level deposits that accumulate to $10,000.00.
- Deposit
- $1,773.96
- Target
- $10,000.00
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In short
- $10,000 in five years at 6 percent needs $1,773.96 a year, less than a fifth of the target.
- The difference is interest: each deposit compounds for the periods remaining after it is made.
- Monthly deposits reach a target more cheaply again: $20,000 in three years at 5 percent needs $516.08 a month.
- The final deposit earns nothing, because it arrives on the target date.
- It is the future value of an annuity, solved for the payment instead of the total.
Working backwards from the date
Most saving questions run forwards: put money away and see what it becomes. A sinking fund runs the other way. The amount and the date are fixed, usually by something real like a bond that matures, a roof that needs replacing or a machine that must be replaced, and the question is what to put aside each period.
Dividing the target by five gives a year, and that is the answer only if the money earns nothing. At 6 percent the deposit is $1,773.96, because the first deposit has four years of growth ahead of it, the second has three, and so on.
The last deposit does no work
In the standard ordinary-annuity version, deposits land at the end of each period, so the final one arrives on the target date and earns nothing at all. Only the earlier deposits compound, which is why the saving from interest is smaller than a naive calculation suggests.
Moving the deposits to the start of each period gives every one of them an extra period of growth, which lowers the required deposit. That is the annuity due variant, and ordinary against due annuity sets out the difference the timing makes.
Frequency does real work
Depositing monthly rather than annually gets money into the fund sooner and gives it more compounding periods. $20,000 over three years at 5 percent needs $516.08 a month, and the total of those payments is below what an annual schedule would require.
The period rate has to match the deposit frequency, which is the point people get wrong. An annual rate applied to monthly deposits will produce a confident and completely wrong answer, so the sinking fund calculator takes frequency as its own input.
Where it is used
Corporate finance uses sinking funds to retire debt gradually, which is where the name comes from. Property owners use them for capital replacement. Households use them without the name for a car, a wedding or school fees. In every case the discipline is the same: name the amount, name the date, then solve for the deposit rather than guessing at it. The savings goal calculator does the same job for a general target, and sinking fund covers the term itself. This is educational material, not financial advice.
Worked examples
\$10,000 in five years at 6 percent
A fund needs to reach $10,000 in five years, earning 6 percent a year, with one deposit at the end of each year. What is the deposit?
- Each deposit compounds for the years remaining after it is made, and the last one earns nothing.
- Solving for the deposit whose compounded total is $10,000 gives $1,773.96.
$1,773.96 a year. Interest covers the rest of the $10,000 target.
\$20,000 in three years, deposited monthly
A target of $20,000 in three years at 5 percent, with monthly deposits.
- The period rate is 5 percent divided by 12, and there are 36 deposits.
- The deposit that reaches $20,000 is $516.08 a month.
$516.08 a month. More frequent deposits mean more compounding periods, so each one can be smaller.
Common questions
Why is the deposit below the target divided by the periods?
Because the deposits earn interest along the way. Only the last one arrives with no time left to grow.
What if the rate is zero?
Then the deposit is exactly the target divided by the number of periods, since nothing compounds.
Is this the same as a savings goal?
The same identity. A sinking fund is the version tied to a specific future obligation.
Is this financial advice?
No. It is educational material about solving for a required deposit.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.