Sinking Fund Calculator

What this sinking fund calculator does

You know what you need and when you need it. A roof replaced in five years. A machine that has to be bought when the current one dies. A bond that matures on a date somebody wrote down decades ago. What you do not know is how much to put aside each time so the money is actually there when the day arrives.

That is the question this answers. You give it the target amount, the interest rate the fund will earn, how often that interest compounds, and how long you have. It returns the contribution you need to make each period, plus the factor it used to get there.

The reason you cannot just divide the target by the number of payments is that the fund earns interest while it fills. That interest does real work, and on a long horizon it does a surprising amount of it.

All of it runs in your browser. Nothing stored, nothing sent.

How to use it

1. Money to accumulate. Your target. What has to be sitting in the fund at the end.
2. Annual interest rate. What the fund earns, as a percentage.
3. Rate Compounding Frequency. Yearly through to daily. This sets both how often interest is added and how often you contribute, which is the thing to understand before you read your answer.
4. Period (Years) and Period (Months). How long you have. Use both fields together for something like three years and six months.

Press Calculate. Press Reset to clear it.

One thing to know about the months field. Extra months are converted into whole compounding periods, so on Yearly compounding anything under twelve months rounds down to nothing and the answer will treat three years and eleven months as three years flat. Pick a more frequent compounding setting and the months are counted properly. On Monthly, every month lands.

Read this before you read your answer

The contribution you get back is per compounding period, not per month and not per year. Which period depends entirely on what you chose in that dropdown.

So if you selected Monthly, the answer is a monthly contribution. Quarterly, it is quarterly. Yearly, it is a single annual payment. Weekly, weekly.

This matters more than it sounds. Ask for 500,000 in five years at 6 percent and the tool will tell you 88,698 on Yearly and 7,166 on Monthly. Those look like wildly different answers to the same question, and they are not. One is a yearly payment and the other is a monthly one. Multiply the monthly by twelve and you get 85,997, which is close to the yearly figure and slightly lower, exactly as more frequent compounding should be.

So set the frequency to match how you actually intend to pay in, then read the number as a payment on that schedule. If you intend to save monthly, choose Monthly.

The sinking fund factor

The whole thing turns on one expression, known in engineering economics as the A/F factor or sinking fund factor. In words, it converts a future lump sum into the equal payments that build it.

A = F × [ i ÷ ((1 + i)ⁿ − 1) ]

Where A is the contribution per period, F is the target amount, i is the periodic interest rate, and n is the number of periods.

The tool works out i by dividing your annual rate by the compounding frequency, and n by multiplying the frequency by your term. The bracketed part is what it labels the USSF factor in the results.

If the shape of that bracket looks familiar, it should. It is the exact reciprocal of the future value of an annuity formula, the one that tells you what a stream of payments grows into. Same relationship, read from the other end. There you know the payment and want the total, here you know the total and want the payment.

Two assumptions ride along with it. Payments land at the end of each period, which is the ordinary annuity convention, so your first contribution arrives one period in rather than today. And the rate holds steady for the whole term.

A worked example: 500,000 in five years

Target 500,000, rate 6 percent, compounding Monthly, term 5 years.

The periodic rate is 0.06 ÷ 12 = 0.005. The number of periods is 12 × 5 = 60.

The factor is 0.005 ÷ (1.005⁶⁰ − 1) = 0.005 ÷ 0.348850 = 0.014333.

So the contribution is 500,000 × 0.014333 = 7,166.40 a month.

Now for the part that makes the exercise worth doing. Sixty payments of 7,166.40 comes to 429,984. But the target was 500,000. The missing 70,016 is interest the fund earned while it was filling, which is 14 percent of the goal that you never had to find yourself.

Put it the other way round. With no interest at all you would need 500,000 ÷ 60 = 8,333.33 a month. The 6 percent rate saves you 1,166.93 every month for five years, which is the clearest possible argument for keeping a sinking fund somewhere that pays interest rather than in a current account.

What the compounding dropdown does to the answer

Same 500,000 target, same 6 percent, same five years, changing only the frequency. The last column is the useful one, because it puts every option on the same annual footing:

Paying in more often costs you less overall, because each contribution starts earning sooner. Moving from yearly to monthly saves about 2,700 a year on this target.

But look at where the savings stop. Yearly to monthly is worth a real amount. Monthly to weekly is worth about 190 a year. Weekly to daily is worth 49. The curve flattens hard, which is a general truth about compounding frequency and a good reason not to agonise over it. Get from yearly to monthly and you have taken almost all of the available benefit.

Three different things get called a sinking fund

Worth untangling, because searching the term throws all three at you at once and they are genuinely different.

The bond provision. A clause requiring an issuer to set money aside, or retire portions of a bond early, so the whole debt does not land at once on maturity. This is the oldest use of the phrase and the one that gave it the name. Investors like it because it lowers default risk.

The asset replacement fund. The engineering economics version, and the one this calculator is built around. A business knows a piece of equipment or a roof or a fleet will need replacing on a schedule, so it accumulates the money in advance rather than facing a sudden capital demand. This is where the A/F factor lives.

The personal budgeting category. The newer use, popular in household budgeting. You know your car insurance is due in November and Eid or Christmas is coming, so you put a fixed amount aside each month. Same idea, smaller numbers, and usually no interest at all.

All three share the same logic: a known cost, a known date, and a decision to spread it rather than be ambushed by it. The maths here serves all three, though for the household version at typical current account rates you may as well divide the target by the number of months and be done with it.

Questions people ask

Is the contribution monthly or yearly?

Whatever you chose in the compounding dropdown. Monthly compounding gives a monthly contribution, yearly gives an annual one. See the section above, it is the most common misreading of this tool.

What is the USSF factor in the results?

The sinking fund factor, more commonly written as the A/F factor. Multiply your target by it and you get the contribution per period. A factor of 0.014333 means each payment is about 1.43 percent of the eventual total.

How is this different from a savings calculator?

Direction. A savings calculator knows your contribution and finds the total. This knows the total and finds the contribution. Same formula, solved for a different unknown.

When is the first payment made?

At the end of the first period, not today. That is the ordinary annuity convention. If you intend to pay at the start of each period instead, your fund will finish slightly ahead of target.

What if my fund earns no interest?

The formula divides by zero at a rate of nothing, so the tool asks for a positive rate. With no interest, just divide the target by the number of payments.

Why did my extra months not change anything?

Because part months are converted into whole compounding periods and rounded down. On Yearly compounding, anything under a full year disappears. Switch to Monthly and every month counts.

Which currency is it in?

The fields are labelled in $and the results print with Rs, but the arithmetic is currency blind. Read the answer in whatever you put in.

References

A note on sourcing. The sinking fund factor is standard engineering economics notation, written as (A/F, i%, n) and derived as the reciprocal of the uniform series compound amount factor. The underlying annuity mathematics, including the end of period convention used here, is set out in the time value of money literature below.

1. OpenStax, Principles of Finance, Section 8.2, Annuities. https://openstax.org/books/principles-finance/pages/8-2-annuities
2. Blank, L. and Tarquin, A., Engineering Economy, 8th edition, McGraw-Hill Education, 2018.
3. National Council of Examiners for Engineering and Surveying, FE Reference Handbook, Engineering Economics section, factor tables for (A/F, i%, n).
4. Kellison, S. G., The Theory of Interest, 3rd edition, McGraw-Hill, 2008.