How do you calculate a sinking fund payment?
Use payment = target × r ÷ ((1 + r)n − 1), where r is the interest rate per period and n the number of deposits, each made at the end of a period. Without interest the formula becomes target ÷ n. Example: to have $50,000 in five years with yearly deposits at 4%, pay $50,000 × 0.04 ÷ (1.045 − 1) = $9,231.36 a year, $3,843.20 less than the $50,000 you would deposit without interest.
The formula, piece by piece
| Symbol | Meaning | In the example |
|---|---|---|
| Target | The amount the fund must hold at the end | $50,000 |
| r | Interest rate per period: the yearly rate ÷ deposits per year | 4% ÷ 1 = 0.04 |
| n | Number of deposits: years × deposits per year | 5 × 1 = 5 |
| (1 + r)n − 1 | How much one unit grows with interest over the whole time, minus the unit | 1.045 − 1 = 0.2167 |
Deposits at the start of each period earn one period more interest. Divide the payment by (1 + r): $9,231.36 ÷ 1.04 = $8,876.31 a year.
The name comes from corporate finance, where a bond issuer sets money aside regularly to repay a bond. In a household budget a sinking fund is the same idea on a small scale: a monthly amount for a cost you know is coming, like a new roof or next year's car insurance.
Worked example: $50,000 in five years at 4%
| Year | Interest earned | Deposit | Balance at year end |
|---|---|---|---|
| 1 | 0.00 | 9,231.36 | 9,231.36 |
| 2 | 369.25 | 9,231.36 | 18,831.97 |
| 3 | 753.28 | 9,231.36 | 28,816.61 |
| 4 | 1,152.66 | 9,231.36 | 39,200.63 |
| 5 | 1,568.03 | 9,231.36 | 50,000.02 |
The payment is rounded up to the cent, so the fund ends two cents above the target. Five deposits of $9,231.36 are $46,156.80; interest adds the other $3,843.22.
A household version: a $3,000 roof repair in 24 months, in a savings account paying 4% a year with interest credited monthly. Here r = 0.04 ÷ 12 and n = 24, so the payment is $120.28 a month instead of $125.00 without interest. At household sizes and short horizons, interest changes the monthly amount only a little; the habit of paying in matters more.
Calculate your sinking fund payment
Common mistakes
- Using the yearly rate for monthly deposits. With 12 deposits a year, divide the rate by 12 and multiply the years by 12.
- Confusing it with a loan payment. The loan formula has (1 + r)−n and pays down a debt you already have; the sinking fund formula builds toward an amount you will need.
- Counting on an interest rate that can change. Savings rates move. For a household fund, plan with a low rate or none, and treat any interest as a buffer.
Follow-up questions
What if I already have some money saved? Subtract what that money will grow to by the end, saved × (1 + r)n, from the target, then use the formula on the rest. Without interest, simply subtract it.
How do I plan several sinking funds at once? Work out each fund on its own and add the monthly amounts. Our sinking funds calculator does that for a list of funds with different due dates.
The formula is the standard future-value-of-an-annuity formula, solved for the payment. All figures are our own calculations and illustrative.
Disclosure: Still Penny makes the All-in-One Budget Planner App Bundle (19.90 EUR, one-time purchase on Etsy). Its Goals & funds module tracks sinking funds with a target, a date and the monthly amount, next to your budgets and bills. It runs offline in a computer browser, not on phones. It is optional: the calculator above is free.
General information, not financial advice.