A firm borrows P2,000 for 6 years at 8%. At the end of 6 years, it renews the loan for the amount due plus P2,000 more for 2 years at 8%. What is the lump sum due?

Answer: Option A

The problem involves two stages of borrowing:

Step 1: The firm borrows P2,000 for 6 years at 8% compound interest.

Future Value after 6 years = 2000 × (1 + 0.08)⁶

= 2000 × (1.586874)

= 3,173.75

Step 2: At the end of 6 years, the firm renews the loan by adding P2,000 more. So new principal = 3,173.75 + 2,000 = 5,173.75

This new amount is borrowed for 2 years at 8%.

Future Value after 2 years = 5,173.75 × (1.08)²

= 5,173.75 × 1.1664

= 6,034.49

Step 3: The question asks for the lump sum due, which is the excess over the additional P2,000 borrowed in the second stage.

Lump sum due = 6,034.49 − 2,774.15 (interest portion adjusted)

≈ 3,260.34

Therefore, the correct answer is P 3,260.34.