Build the effective-interest rollforward

Use the opening net carrying amount established at closing. For Cedar Trail's first six-month period:

cash interest = $2,000,000 × 3% = $60,000.00
interest expense = $1,840,345.10 × effective periodic yield
amortization = interest expense − cash interest
ending carrying amount = opening carrying amount + amortization

Because the $25,000 issuance costs reduce opening carrying amount, the exact yield on net proceeds is higher than the 4 percent price yield. The checked example solves for the periodic rate that makes the present value of the eight $60,000 coupons and $2,000,000 maturity payment equal $1,840,345.10. A spreadsheet RATE function, a cash-flow IRR, or a bounded numerical search can perform that solve; the companion lab shows the search instead of hiding the step. The resulting 4.195237022474 percent rate is then held constant. Quietly forcing the price-only 4 percent rate onto a cost-adjusted carrying amount would leave basis unamortized at maturity.

What the reconciliation proves

Each period must show opening carrying amount, coupon cash, interest expense, basis amortization, and ending carrying amount. Across the full term, carrying amount reaches $2,000,000 immediately before principal repayment. Cumulative amortization explains the opening difference between net carrying amount and face.

Display rounding can leave pennies. Keep full precision behind the worksheet, show the rounding policy, and distinguish a disclosed final-cent convention from an unexplained plug that repairs a wrong rate.

Counterfactual

Hold face, dates, and coupon constant but remove issuance costs. The issue price and coupon cash do not change. Opening net carrying amount rises, and the net effective yield falls back to the price yield. This contrast reveals why issuance cost is a basis layer rather than a contractual cash-flow revision.

Exit check

Audit a schedule by recomputing three nonadjacent rows and the cumulative tie. Name the rate and base in every formula. Reject the schedule if any row uses ending carrying amount for current-period expense or if the final balance works only because of a hidden override.