FDNBUSM 05 · Sinking Funds and Funding Schedules

R = F/s(i,n)

Sinking funds accumulate future deposits to a future target. The PV factor instead prices a current loan obligation.

R = [F − P(1 + i)^n]/s(i,n)

Accumulate the existing balance to the target date, subtract it from the future requirement, then fund the residual with the annuity.

Its first deposit arrives only at the end of that period.

The opening balance is zero throughout period 1. Beginning-of-period deposits would earn first-period interest.

Closing balance = B(1 + i) + R

Opening balance earns the period interest; the deposit is added at the end and earns nothing in that period.

4%, the fund yield

The reserve grows at its own earned yield. The 6% debt rate determines borrowing interest, not deposit growth.

No; they build a separate asset until used to repay debt.

Debt face amount and accumulated reserve are distinct. Face less reserve may measure net unfunded debt, but the lender still holds the contractual claim.

R(1 + i)^(n−k)

The missed deposit would have grown from period k to period n, a total of n − k periods.

FV increases, so a fixed target could be funded with a smaller R.

Each deposit’s future growth weakly increases, and earlier deposits earn more. For n > 1 and positive yield changes, total FV increases.

12

The first eight deposits are already embodied in the current balance. The next deposit occurs one interval after review.

Final deposit = target − B(1 + i)

Accumulate the actual prior balance through the final period, then fill the remaining gap. Do not apply a blanket rounding correction without the actual balance.