Sinking-Fund Factor (A/F)

A = F [\frac{i}{( 1 + i ) ^{n} - 1}] = F (A / F, i, n)

Uniform deposit A that will accumulate to a future amount F in n periods. Reciprocal of F/A.

Step-by-step solved example

What annual deposit at 6% accumulates to $10,000 in 5 years?

Uniform A that will equal a target F (sinking fund).

1. Factor
(A/F, 6%, 5) = 0.06/[(1.06)^5 − 1] = 0.1774.
$(A / F, 6%, 5) = 0.1774$
2. Deposit
A = 10000 × 0.1774 = $1,774.
$A = 1774$

Answer: A = $1,774 / yr

0/10 correct

1.(A/F, 10%, 2) equals

2.A to reach F = $2,100 in 2 years at 10% is

3.A/F is used to fund a future

4.If i = 0, A/F equals

5.Larger i means, for fixed F and n, A is

6.(A/F, i, 1) equals

7.A/F × F/A equals

8.F = $5,000, i = 0%, n = 5 → A =

9.Sinking-fund deposits are assumed

10.To convert a future overhaul cost into an equivalent annual cost, use