Sinking Funds: How They Work and Exam FM Calculations

Sinking Fund Method

Under the sinking fund method, the borrower pays interest-only on the loan each period (interest at rate i on the original loan L) and simultaneously deposits into a sinking fund that earns rate j to accumulate to L at the end of n periods. The sinking fund deposit is D = L / s-angle-n at rate j. The total periodic outlay is L*i + L/s-angle-n(j).

When i = j, the total outlay equals the amortization payment: L*i + L/s-angle-n(i) = L/a-angle-n(i). This identity connects the sinking fund and amortization methods.

Sinking Fund Schedule

The sinking fund balance after t deposits is D * s-angle-t at rate j. The net amount owed (book value of the loan) is L - D * s-angle-t. The "principal" repaid in year t is the increase in the sinking fund: D*(1+j)^(t-1), which is the interest earned on the sinking fund plus the deposit minus the previous period's interest.

When i > j, the total periodic outlay under the sinking fund method exceeds the amortization payment. When i < j, it is less. This comparison is a common Exam FM question.

Exam FM Problem Types

Typical problems ask you to compare the total annual cost of a sinking fund arrangement versus amortization, find the sinking fund balance at a specific time, or determine the net loan balance. Remember that the sinking fund grows independently from the loan, so the interest on the loan and the interest on the sinking fund may be at different rates. Always identify both rates before setting up your equations.