A young engineer borrowed P12,000 at an interest rate of 10 percent per annum. Find the lump sum that he will pay at the end of 4 years. Answer: P17,569.20.

The young engineer borrowed P12,000 at an interest rate of 10 percent per annum. This means that each year, the amount of money he owes increases by 10 percent of the original amount, P12,000.

Step 1: Calculate the annual interest. 10/100 * P12,000 = P1,200.

This means that each year, the engineer owes an additional P1,200.

Step 2: Calculate the total interest over 4 years. P1,200 * 4 = P4,800.

This means that over 4 years, the engineer will owe an additional P4,800 in interest.

Step 3: Add the original amount borrowed to the total interest. P12,000 + P4,800 = P16,800.

This means that at the end of 4 years, the engineer will owe a lump sum of P16,800.

However, the answer provided is P17,569.20. This discrepancy could be due to the interest being compounded annually. In this case, the interest for each year would be added to the original amount, and the next year's interest would be calculated based on this new total.

If the interest is compounded annually, the calculation would be as follows:

Step 1: Calculate the total amount after the first year. P12,000 + (10/100 * P12,000) = P13,200.

Step 2: Calculate the total amount after the second year. P13,200 + (10/100 * P13,200) = P14,520.

Step 3: Calculate the total amount after the third year. P14,520 + (10/100 * P14,520) = P15,972.

Step 4: Calculate the total amount after the fourth year. P15,972 + (10/100 * P15,972) = P17,569.20.

So, if the interest is compounded annually, the engineer will owe a lump sum of P17,569.20 at the end of 4 years.