Number and Algebra

Loans: Pag-IBIG, motorcycle financing and 5-6

Financial mathematics

Mga pautang: Pag-IBIG, hulugan ng motor at 5-6

Compare how a housing loan, a motorcycle instalment plan and informal '5-6' lending actually charge interest, and what a borrower really pays.

Where it fits

Business and Consumer Loans · Term 3 · Week 4
Sequences in Finance · Term 1 · Week 5

Competencies

gm11.t3.w4.c1 Differentiate between business and consumer loans and their characteristics, such as repayment terms, requirements, purpose, and interest rates.
gm11.t3.w4.c2 Solve problems involving business and consumer loans (e.g., amortization, mortgage).
gm11.t1.w5.c1 Apply sequences and series to solve financial problems, such as periodic payments for loans and mortgages.

The data

Three ways to borrow ₱10,000 for 6 months
Lender	Stated rate	How interest is computed	Interest on ₱10,000 for 6 months	Requirements
Pag-IBIG multi-purpose loan	10.5% per year	Diminishing balance, monthly	₱310	Member with 24 contributions
Bank personal loan	1.5% per month add-on	Simple interest on full principal	₱900	Payslip, ID, good credit
Cooperative loan	2% per month add-on	Simple interest on full principal	₱1,200	Co-op membership
'5-6' informal lender	20% per month	Simple interest, collected daily	₱12,000	None

Interest on ₱10,000 for 6 months by Lender

Source: Representative 2026 figures for classroom use; check current official rates before using for real decisions. Pag-IBIG and bank rates are published ranges; 5-6 terms are what borrowers commonly report.

Scenario and worked example

The tricycle that pays for itself?

Engage

Mang Ben drives a rented tricycle and keeps ₱400 a day after boundary and fuel. A dealer offers a new unit for ₱78,000: 20% down, the balance at 1.5% per month add-on for 24 months. A 5-6 lender offers the down payment for 20% a month. Should he borrow?

Worked example: the add-on loan

Explain

Add-on interest is charged on the original balance for the whole term, even as it is paid down.

\text{Financed} = 78{,}000 \times 0.80 = 62{,}400

I = Prt = 62{,}400 \times 0.015 \times 24 = 22{,}464

\text{Monthly} = \frac{62{,}400 + 22{,}464}{24} = 3{,}536

Compare with diminishing balance

Elaborate

A bank or Pag-IBIG loan charges interest only on what is still owed, so the same stated rate costs much less. The amortisation formula used by banks is

R = \frac{P\,i}{1-(1+i)^{-n}}

Reading the fine print

Evaluate

Add-on rate of 1.5%/month is roughly 32% per year effective, not 18%.
'Zero interest' instalments often hide a higher cash price.
5-6 means borrow 5, pay 6: 20% per month, about 240% per year.

Discuss in class

Why does the same 'per month' rate cost different amounts in the table?
Mang Ben earns ₱400 a day net. Can he afford ₱3,536 a month? What risks does he face?
Why do people still borrow from 5-6 lenders when cooperatives are cheaper?
What questions should you ask before signing any loan agreement?

Problems

6 problems · check your answer, then open the solution

Problem 1 Basic

A motorcycle costs ₱78,000. The buyer pays a 20% down payment and finances the rest. How much is financed?

Your answer (₱)
Show step-by-step solution
1. Down payment: $0.20 \times 78{,}000 = 15{,}600$ .
2. Amount financed: $78{,}000 - 15{,}600 = 62{,}400$ pesos.
Answer: 62400 ₱
Problem 2 Standard

The ₱62,400 balance on a motorcycle is financed at an add-on rate of 1.5% per month for 24 months. Find the monthly payment.

Your answer (₱)
Show step-by-step solution
1. Add-on interest is simple interest on the whole balance: $I = 62{,}400 \times 0.015 \times 24 = 22{,}464$ .
2. Total to repay: $62{,}400 + 22{,}464 = 84{,}864$ .
3. Monthly payment: $84{,}864 \div 24 = 3{,}536$ pesos.
Answer: 3536 ₱
Problem 3 Standard

A sari-sari store owner borrows ₱5,000 from a '5-6' lender and must repay ₱6,000 after one month. What is the monthly interest rate, in percent?

Your answer (%)
Show step-by-step solution
1. Interest paid: $6{,}000 - 5{,}000 = 1{,}000$ .
2. Rate $= \dfrac{1{,}000}{5{,}000} = 0.20 = 20\%$ per month.
3. That is $20\% \times 12 = 240\%$ per year as simple interest, far above any bank rate.
Answer: 20 %
Problem 4 Basic

Which of the following is a business loan rather than a consumer loan?

Choices a. A loan to buy a family motorcycle b. A Pag-IBIG housing loan for the family home c. A loan to buy a second tricycle to rent out to a driver d. A credit card purchase of a phone
Show step-by-step solution
1. A business loan funds an activity that earns income (the tricycle will be rented out).
2. The motorcycle, house and phone are for personal use, so those loans are consumer loans.
Answer: c
Problem 5 Challenge Non-routine

A Pag-IBIG housing loan of ₱1,000,000 is amortised over 20 years at 6.25% per year, compounded monthly. Use $R = \dfrac{P\,i}{1-(1+i)^{-n}}$ with $i=\dfrac{0.0625}{12}$ and $n=240$ . Find the monthly amortisation to the nearest peso.

Your answer (₱)
Show step-by-step solution
1. $i = 0.0625/12 \approx 0.0052083$ and $n = 20 \times 12 = 240$ .
2. $(1+i)^{-240} \approx 0.28715$ , so $1-(1+i)^{-n} \approx 0.71285$ .
3. $R = \dfrac{1{,}000{,}000 \times 0.0052083}{0.71285} \approx 7{,}309$ pesos per month.
4. Over 240 months the borrower pays about ₱1.75 million, so interest is about ₱754,000.
Answer: 7309 ₱
Problem 6 Challenge Non-routine

Aling Nena needs ₱10,000 for six months. A '5-6' lender charges 20% per month simple interest; a cooperative charges 2% per month add-on. How much more interest does the 5-6 loan cost?

Your answer (₱)
Show step-by-step solution
1. 5-6: $10{,}000 \times 0.20 \times 6 = 12{,}000$ in interest.
2. Cooperative: $10{,}000 \times 0.02 \times 6 = 1{,}200$ in interest.
3. Difference: $12{,}000 - 1{,}200 = 10{,}800$ pesos.
Answer: 10800 ₱

Loan and interest calculator More practice: Business and Consumer Loans More practice: Sequences in Finance