Final answer:
Ola's capital balance after investing P1,000,000 for a 1/4 interest in the partnership will be P1,000,000. A bonus to the existing partners is calculated based on the total value of the partnership post-investment, but Ola's capital account is not affected by this bonus.
Step-by-step explanation:
The question pertains to the admission of a new partner, Ola, into an existing partnership between Berns and Ruiz. To determine Ola's capital balance after investing P1,000,000 for a 1/4 interest in the partnership, we must first find the total value of the partnership prior to Ola's admission. As Ola is obtaining a 1/4 interest by contributing P1,000,000, this implies that the total value of the partnership is P1,000,000 divided by 1/4, which equals P4,000,000. As Berns and Ruiz have existing capital balances totaling P3,500,000 (P2,000,000 + P1,500,000), the implied value of their partnership is less than P4,000,000; this indicates that a bonus to the existing partners is required for the admission of Ola.
To calculate the bonus, we subtract the existing partners' capital from the total value post Ola's investment: P4,000,000 - P3,500,000 = P500,000. This bonus is shared between Berns and Ruiz in their profit and loss ratio of 3:2. The proportion of the bonus for each partner is P300,000 to Berns and P200,000 to Ruiz. Therefore, Ola's actual capital account is Ola's investment minus their portion of the bonus (which is zero, since they are new), so Ola's capital balance after investment will be the full P1,000,000 contributed.