Matematikang pampinansyal

ILAW Daily Lesson Log (DLL)

Compound Interest: Growing Money Over Time

Compound Interest · Term 3 · Week 1

Word (.docx)

Learning area: General Mathematics
Designed by: SSHS Math Talas Hub
Grade level and section: Grade 11
Sessions / term: 3 sessions · Term 3
References: DepEd Grade 11 Three-Term Budget of Work (BOW) for General Mathematics
Bangko Sentral ng Pilipinas (BSP) consumer guides on savings and time deposits
Published savings and time-deposit rate sheets of local banks and cooperatives
Galamay, D.O., & Albay, E.M. (2026). General Mathematics: A Strengthened Senior High School Textbook. Diwa Learning Systems Inc.
Digital tools: Google Sheets, Calculator, Desmos
Declaration of AI use (DO 3, s. 2026 Annex A): AI was used only as an auxiliary support tool in preparing and improving this lesson plan, in accordance with DepEd Order No. 003, s. 2026. The teacher retained human judgment and full responsibility for content selection, contextualization, assessment decisions, learner feedback, and final approval. AI-generated suggestions were reviewed, edited, and checked for accuracy, bias, appropriateness, data privacy, and alignment with the Learning Competencies. No learner personal data were entered into AI tools, and AI will not be used as the sole basis for grading, learner evaluation, disciplinary decisions, or other major academic decisions.

Intentions

Learning competency

Solve problems involving compound interest, including maturity value, future value, nominal rates, and number of terms.

gm11.t3.w1.c1

Learning objectives

At the end of the 45-minute period, the learners should be able to:

distinguish simple from compound interest by building year-by-year tables;
derive the compound-interest formula from repeated multiplication; and
appreciate time as a factor in growing savings.

Learner context

Learners computed simple interest and geometric sequences in Term 1 and can enter formulas in a spreadsheet. They tend to think of interest as a fixed yearly amount and expect simple and compound interest to differ only slightly. Many families use cooperatives, paluwagan or bank savings, which gives concrete anchors.

Learning experience

Pre-lesson

Hook

Engage

You have ₱10,000 for 10 years. Offer A pays 5% simple interest; Offer B pays 5% per year added to your balance. Guess the difference in the final amounts.

Activity: Retrieve and Connect

Elicit

Recall the simple-interest formula and the pattern of a geometric sequence with ratio 1.05. Learners write both from memory.

I = Prt

a_n = a_1 r^{n-1}

Flow

Explore: Build the two tables

Explore

In Google Sheets (or on paper), groups build year-by-year balances for both offers for 10 years, then extend to 30 years. They record when the gap first exceeds ₱1,000 and ₱10,000.

Year	Offer A (simple)	Offer B (compound)
0	10,000.00	10,000.00
1	10,500.00	10,500.00
2	11,000.00	11,025.00
3	11,500.00	11,576.25
10	15,000.00	16,288.95
30	25,000.00	43,219.42

Explain: From the table to the formula

Explain

Ask: 'What did you multiply by each year? How many times after n years?' Build the formula from the repeated factor, and connect to the geometric sequence from Term 1.

F = P(1 + j)^n

16{,}288.95 = 10{,}000(1.05)^{10}

Elaborate: Graph it

Elaborate

Groups graph both offers in Desmos (y = 10000 + 500x and y = 10000(1.05)^x). Describe the shapes: linear vs exponential. Ask: 'Where do they cross? Why does the gap keep growing?'

Learning resources

Google Sheets (or grid paper)
Desmos or graphing calculator
Calculator
Compound-interest exploration sheet

Opportunities for integration

ICT: Spreadsheet fill-down formulas and Desmos graphing.
Financial Literacy: Why starting to save early matters.
Science: Exponential growth in populations and decay.

Assessment

Formative assessment

Exit Ticket

Evaluate

₱5,000 at 4% compounded annually for 3 years: write the expression, compute the maturity value, and state the compound interest earned.

Accommodation: provide a partially filled table and allow calculator use.

Ways forward

Extended learning opportunities

Interview a Saver

Extend

Ask a family member where they save money (bank, cooperative, paluwagan, none) and what interest, if any, they receive. Bring one rate to class.

Reflections

Think about what you need to change for the next session based on what happened today.

Day 1

Intentions

Learning competency

Solve problems involving compound interest, including maturity value, future value, nominal rates, and number of terms.

gm11.t3.w1.c1

Learning objectives

At the end of the 45-minute period, the learners should be able to:

distinguish simple from compound interest by building year-by-year tables;
derive the compound-interest formula from repeated multiplication; and
appreciate time as a factor in growing savings.

Learner context

Learning experience

Pre-lesson

Hook

Engage

You have ₱10,000 for 10 years. Offer A pays 5% simple interest; Offer B pays 5% per year added to your balance. Guess the difference in the final amounts.

Activity: Retrieve and Connect

Elicit

Recall the simple-interest formula and the pattern of a geometric sequence with ratio 1.05. Learners write both from memory.

I = Prt

a_n = a_1 r^{n-1}

Flow

Explore: Build the two tables

Explore

In Google Sheets (or on paper), groups build year-by-year balances for both offers for 10 years, then extend to 30 years. They record when the gap first exceeds ₱1,000 and ₱10,000.

Year	Offer A (simple)	Offer B (compound)
0	10,000.00	10,000.00
1	10,500.00	10,500.00
2	11,000.00	11,025.00
3	11,500.00	11,576.25
10	15,000.00	16,288.95
30	25,000.00	43,219.42

Explain: From the table to the formula

Explain

Ask: 'What did you multiply by each year? How many times after n years?' Build the formula from the repeated factor, and connect to the geometric sequence from Term 1.

F = P(1 + j)^n

16{,}288.95 = 10{,}000(1.05)^{10}

Elaborate: Graph it

Elaborate

Groups graph both offers in Desmos (y = 10000 + 500x and y = 10000(1.05)^x). Describe the shapes: linear vs exponential. Ask: 'Where do they cross? Why does the gap keep growing?'

Learning resources

Google Sheets (or grid paper)
Desmos or graphing calculator
Calculator
Compound-interest exploration sheet

Opportunities for integration

ICT: Spreadsheet fill-down formulas and Desmos graphing.
Financial Literacy: Why starting to save early matters.
Science: Exponential growth in populations and decay.

Assessment

Formative assessment

Exit Ticket

Evaluate

₱5,000 at 4% compounded annually for 3 years: write the expression, compute the maturity value, and state the compound interest earned.

Accommodation: provide a partially filled table and allow calculator use.

Ways forward

Extended learning opportunities

Interview a Saver

Extend

Ask a family member where they save money (bank, cooperative, paluwagan, none) and what interest, if any, they receive. Bring one rate to class.

Reflections

Think about what you need to change for the next session based on what happened today.

Day 2

Intentions

Learning competency

Solve problems involving compound interest, including maturity value, future value, nominal rates, and number of terms.

gm11.t3.w1.c1

Learning objectives

At the end of the 45-minute period, the learners should be able to:

convert a nominal annual rate into a periodic rate and count the number of periods;
compute maturity values for monthly, quarterly and semi-annual compounding; and
justify why more frequent compounding yields more at the same nominal rate.

Learner context

Learners can apply F = P(1 + j)^n with annual compounding. The idea that '6% per year compounded monthly' means 0.5% twelve times is new, and the usual error is to use 6% as the monthly rate. Bank rate sheets brought from home make the vocabulary (nominal, per annum, compounded quarterly) authentic.

Learning experience

Pre-lesson

Hook

Engage

Two banks both advertise '6% per annum'. One compounds yearly, the other monthly. Is one offer better? By how much on ₱20,000 for 5 years?

Activity: Predict

Elicit

Learners write a prediction and a reason before computing.

Flow

Explore: Chop the year

Explore

Groups model 6% compounded monthly on ₱20,000 for one year in Sheets, month by month, with the rate 0.06/12 per month. Compare the end-of-year balance with 6% once. Then repeat for quarterly and semi-annual.

Compounding	m	j = i/m	n for 5 years	F on ₱20,000
Annually	1	0.06	5	26,764.51
Semi-annually	2	0.03	10	26,878.33
Quarterly	4	0.015	20	26,937.10
Monthly	12	0.005	60	26,977.00

Explain: Periodic rate and number of periods

Explain

Formalise j = i/m and n = mt. Emphasise reading a rate sheet: 'nominal rate', 'per annum', 'compounded quarterly'.

j = \dfrac{i}{m},\quad n = mt

F = P\left(1 + \dfrac{i}{m}\right)^{mt}

Elaborate: Which Student Is Correct?

Elaborate

Student A computes ₱20,000(1.06)^60 for monthly compounding over 5 years. Student B computes ₱20,000(1.005)^60. Student C computes ₱20,000(1.005)^5. Decide and explain each error.

Learning resources

Google Sheets
Bank or cooperative rate sheets (brought by learners or printed)
Calculator
Periodic-rate worksheet

Opportunities for integration

ICT: Modelling compounding frequency in a spreadsheet.
Financial Literacy: Reading savings and time-deposit offers.
Critical Thinking: Diagnosing errors in peers' solutions.

Assessment

Formative assessment

Exit Ticket

Evaluate

₱12,000 at 8% compounded quarterly for 3 years. State j, n, and the maturity value. Then write one sentence on why quarterly beats annual at the same nominal rate.

Accommodation: formula card with j and n defined; calculator allowed.

Ways forward

Extended learning opportunities

Rate Sheet Decoder

Extend

Take the rate your family member gave you (or a published one) and compute what ₱5,000 becomes in 2 years. Write the j and n you used.

Reflections

Think about what you need to change for the next session based on what happened today.

Day 3

Intentions

Learning competency

Solve problems involving compound interest, including maturity value, future value, nominal rates, and number of terms.

gm11.t3.w1.c1

Learning objectives

At the end of the 45-minute period, the learners should be able to:

find the present value needed to reach a target amount;
determine the number of periods needed to reach a target by systematic guess-and-check; and
recommend a savings plan with justified assumptions.

Learner context

Learners can compute maturity values for any compounding frequency. Working backwards (present value, number of periods) is new and requires reversing the multiplication. They are ready for a performance task comparing authentic offers.

Learning experience

Pre-lesson

Hook

Engage

A Grade 11 learner wants ₱50,000 for a laptop in 3 years. How much must she deposit now at 4% compounded quarterly? How long if she can only deposit ₱40,000?

Flow

Explore: Reverse the growth

Explore

Pairs undo the multiplication to find P, then build a column of (1.01)^n in Sheets to find the smallest n that reaches the target with ₱40,000.

P = \dfrac{F}{(1 + j)^n} = \dfrac{50{,}000}{(1.01)^{12}} \approx 44{,}372.44

Explain: Present value and number of terms

Explain

Consolidate the present-value formula and the guess-and-check (or spreadsheet) approach for n. Mention that logarithms give n directly and will appear in later mathematics.

P = F(1 + j)^{-n}

Performance Task: Savings Plan Comparison

Elaborate

Groups receive three offers (e.g., 5% compounded annually with no fees; 4.8% compounded monthly with a ₱100 annual fee; a cooperative paying 6% simple interest). For ₱15,000 over 5 years they compute every maturity value, chart them, and write a recommendation stating assumptions.

Gallery Walk and Defense

Evaluate

Groups post their comparison; peers use the rubric to ask at most two questions each. Groups defend or revise their recommendation.

Learning resources

Offer cards (three savings products)
Google Sheets or Desmos
Rubric and gallery-walk form
Calculator

Opportunities for integration

ICT: Spreadsheet comparison and charting.
Financial Literacy: Choosing among real savings products; fees and minimum balance.
Communication: Writing a justified recommendation.

Assessment

Formative assessment

Rubric-scored report

Evaluate

The comparison report and defense are scored with the rubric. Exit question: 'Which offer wins for 1 year instead of 5? Does the answer change?'

Ways forward

Extended learning opportunities

Start Small

Extend

If you saved ₱50 a week in a product paying 4% compounded annually, estimate your balance after 5 years (use yearly deposits of ₱2,600 and a table). What would change if you started at Grade 7?

Reflections

Think about what you need to change for the next session based on what happened today.

Rubric: Savings plan comparison report

Criteria	Weight
Correct maturity values for each offer	30%
Correct use of periodic rate and number of periods	20%
Spreadsheet or graph that supports the comparison	20%
Justified recommendation with assumptions stated	20%
Clarity and accuracy of presentation	10%
Total	100%

Teaching notes and common misconceptions

Learners confuse the nominal annual rate with the rate per period. Always write j = i/m explicitly before substituting; 6% compounded monthly is 0.5% per month, not 6% per month.
Exponents are often applied to the whole product P(1 + j) instead of to (1 + j) only. Have learners build the table row by row first so the exponent emerges as 'the number of times we multiplied'.
Simple interest grows linearly and compound interest exponentially; the difference is tiny for a few periods, so learners conclude 'they are the same'. Extend the table to 20–30 years or graph both in Desmos.
When solving for n, learners try to divide by (1 + j). Treat n as 'how many multiplications' and let them guess and check with the spreadsheet before introducing logarithms (optional, not in the BOW).
Rounding each period to centavos in the table gives a maturity value a few centavos off the formula value. Discuss which one a bank uses.