Short answer. Yes. When the business continues without settling accounts, the retired or deceased partner — or his estate — may take, in lieu of interest, the profits attributable to the use of his right in the property of the dissolved partnership. The choice belongs to him or his legal representative.
What the law says
an amount equal to the value of his interest in the dissolved partnership with interest, or, at his option or at the option of his legal representative, in lieu of interest, the profits attributable to the use of his right in the property of the dissolved partnership
Civil Code, Article 1841 — Retiring/Deceased Partner's Interest When Business Continues. Read the full provision →
The situation the article addresses
Article 1841 applies where a partner retires or dies and the others carry on the business without any settlement of accounts between them and the outgoing partner or his estate. Rather than winding the firm down, the survivors keep using the whole of the partnership property — including the departed partner's share of it. The law does not leave that partner empty-handed. It lets him, or his legal representative, have the value of his interest fixed as of the date of dissolution, and it gives him a defined way to be compensated for the continued use of that interest while it stays in the business.
Interest or profits — the estate chooses
The outgoing partner receives, as an ordinary creditor, an amount equal to the value of his interest with interest, or, at his option or his representative's option, in lieu of interest, the profits attributable to the use of his right in the property of the dissolved partnership. That option is the answer to the question. The estate is not confined to a fixed interest rate. If the continuing business earned well by using the departed partner's share, the estate may claim the profits traceable to that use instead. If interest would yield more, it can take interest. The election is the estate's to make, not the surviving partners'.
Creditors of the old firm come first
The right is real but it is not first in line. The article gives the creditors of the dissolved partnership priority on any claim arising under this article as against the separate creditors, or the representative, of the retired or deceased partner. In plain terms, debts the old partnership owed are paid ahead of the outgoing partner's estate. The estate stands as an ordinary creditor of the continuing business for the value of the interest, but behind the firm's own creditors. That ordering matters when the continuing business does not have enough to satisfy everyone at once.
What the estate should do
Two things drive the outcome: the value of the interest at the date of dissolution, and, if profits are chosen, how much of the continuing firm's earnings are fairly attributable to the use of that interest. Both are questions of evidence, so the estate should secure the partnership's books, the dissolution date, and records of the business after the partner left. The phrase unless otherwise agreed also matters — a partnership or buy-out agreement may set a different method, and a valid agreement will govern. Because the numbers and any prior agreement decide everything, close review of the documents is essential.