What is the sinking fund formula?

P = FV × r ÷ [(1 + r)n − 1], where FV is the target, r the interest rate per period and n the number of deposits.

How is a sinking fund different from a loan payment?

A loan payment repays an amount borrowed today (a present value); a sinking fund payment builds up an amount needed later (a future value).

Are deposits at the start or end of each period?

At the end. With start-of-period deposits, divide the payment by (1 + r).

What is a sinking fund in bonds?

A provision where the issuer sets aside money regularly, or retires part of the issue each year, so that the debt can be repaid at maturity.

Sinking Fund Formula and Calculator

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Sinking Fund Payment Calculator

A sinking fund is money set aside in regular instalments to meet a known future cost: repaying a bond at maturity, replacing equipment, a roof, a car or a tuition bill. The sinking fund formula works out the level deposit P that, invested at rate r per period, grows to the target FV after n deposits. It is the future value of an annuity formula solved for the payment.

Formula

P = FV × r(1 + r)ⁿ − 1

Where

P: deposit needed at the end of each period
FV: target amount
r: interest rate per period = annual rate ÷ deposits per year
n: number of deposits = years × deposits per year

Calculator

Target amount (FV)

Annual interest rate (%)

Years

Deposits per year

Result and step-by-step solution

Deposit per period

305.10

120 monthly deposits total 36,612.30; interest supplies the other 13,387.70.

Rate and number of periods
r = 0.06 ÷ 12 = 0.005; n = 10 × 12 = 120
Future value factor
(1 + r)ⁿ − 1r = 1.81939673 − 10.005 = 163.879347
Divide the target by the factor
P = 50,000.00163.879347 = 305.10

How to use the formula

Enter the target, the annual rate, the number of years and how often you will deposit. The calculator converts to a rate per period and a number of deposits, computes the future value factor [(1 + r)ⁿ − 1] ÷ r, and divides the target by it. It also splits the target into what you pay in and what interest contributes.

To collect 50,000 in 10 years at 6% with monthly deposits, you need 305.10 a month. You pay in 36,612.30 and interest supplies the remaining 13,387.70. Compare the same goal with deposits at the start of each month using the annuity due page, or see what a fixed deposit builds with the future value of an annuity.

Frequently asked questions

What is the sinking fund formula?: P = FV × r ÷ [(1 + r)ⁿ − 1], where FV is the target, r the interest rate per period and n the number of deposits.
How is a sinking fund different from a loan payment?: A loan payment repays an amount borrowed today (a present value); a sinking fund payment builds up an amount needed later (a future value).
Are deposits at the start or end of each period?: At the end. With start-of-period deposits, divide the payment by (1 + r).
What is a sinking fund in bonds?: A provision where the issuer sets aside money regularly, or retires part of the issue each year, so that the debt can be repaid at maturity.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.