Question 1

Maria borrowed ₱350,000 from a bank to start a small business. She will repay the loan through fixed monthly payments over 10 years. Since the bank computes the unpaid balance using compound interest, which mathematical concept best describes how the remaining loan balance changes over time?

Accepted Answer

Geometric sequence because the balance changes by a constant percentage as interest is applied

Answer

Fibonacci sequence because each month's balance is the sum of the two previous balances

Answer

Arithmetic series because the monthly payments are added to determine the remaining balance

Answer

Arithmetic sequence because the balance decreases by a fixed amount every month

Question 2

Angela is comparing two savings plans. Plan A requires her to save ₱2,000 every month, while Plan B starts at ₱1,500 per month and increases by ₱200 every six months. Which mathematical strategy will best help Angela determine which plan will result in greater total savings after 3 years?

Accepted Answer

Identify the type of sequence for each savings plan and compute the total amount using a series.

Answer

Select the plan with the higher first deposit without calculating the total savings.

Answer

Multiply the initial monthly deposit by the number of months for both plans.

Answer

Compare only the first monthly deposit of each plan.

Question 3

Ben borrowed ₱150,000 to renovate his house. The bank charges 1.5% monthly interest, and he pays ₱6,000 every month. After 4 months, a student computed the remaining balance by subtracting ₱24,000 from ₱150,000. How should you evaluate the student's solution?

Accepted Answer

Incorrect because the monthly interest must also be included in computing the remaining balance.

Answer

Correct because the loan balance always decreases by a constant amount.

Answer

Incorrect because the remaining balance follows a Fibonacci sequence.

Answer

Correct because the monthly payments are subtracted from the principal only.

Question 4

A learner calculated the accumulated value of an investment using the series:

₱12,000 + ₱13,200 + ₱14,520 + ₱15,972

The learner concluded that the total accumulated value is ₱55,692. What should you conclude after checking the common ratio and the sum?

Accepted Answer

The solution is correct because the common ratio is 1.10 and the sum is ₱55,692.

Answer

The solution is incorrect because the common ratio is 1.10 and the sum is ₱54,692.

Answer

The solution is incorrect because the common ratio is 1.20 and the sum is ₱54,692.

Answer

The solution is correct because the common ratio is 1.20 and the sum is ₱55,692.

Question 5

A learner calculated the accumulated value of an investment using the series:

₱15,000 + ₱16,500 + ₱18,150 + ₱19,965

The learner concluded that the total accumulated value is ₱69,615. Is the computation correct?

Accepted Answer

Yes, because the common ratio is 1.10 and the sum is ₱69,615.

Answer

Yes, because the common ratio is 1.15 and the sum is ₱69,615.

Answer

No, because the common ratio is 1.15 and the sum is ₱68,615.

Answer

No, because the common ratio is 1.10 and the sum is ₱68,615.

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