Number and Algebra

Compound interest: watching ₱10,000 grow

Matematikang pampinansyal

Compound interest: paglago ng ₱10,000

A year-by-year table of a single deposit shows why compound growth starts slow and then accelerates, and how to read nominal versus effective rates.

Where it fits

Compound Interest · Term 3 · Week 1
Sequences in Finance · Term 1 · Week 5

Competencies

gm11.t3.w1.c1 Solve problems involving compound interest, including maturity value, future value, nominal rates, and number of terms.
gm11.t1.w5.c2 Determine the accumulated values of investment over time using sequences and series.

The data

₱10,000 at 6% per year, compounded annually
Year	Simple interest value	Compound value	Interest this year (compound)
0	₱10,000	₱10,000	—
1	₱10,600	₱10,600	₱600
2	₱11,200	₱11,236	₱636
3	₱11,800	₱11,910	₱674
4	₱12,400	₱12,625	₱715
5	₱13,000	₱13,382	₱757
6	₱13,600	₱14,185	₱803
7	₱14,200	₱15,036	₱851
8	₱14,800	₱15,938	₱902
9	₱15,400	₱16,895	₱957
10	₱16,000	₱17,908	₱1,013

Compound value by Year

Source: Computed with A = P(1 + r)^t; rounding to the nearest peso.

Scenario and worked example

Lolo's time deposit

Elicit

When Nico was born his lolo placed ₱10,000 in a time deposit at 6% per year and never touched it. Nico is now in Grade 11. How much is in the account? Why is the yearly interest no longer ₱600?

Worked example

Explain

A = 10{,}000(1.06)^{16} \approx 10{,}000 \times 2.5404 = 25{,}404

\text{Interest in year 16 alone: } 25{,}404 - 23{,}966 \approx 1{,}438

Compound interest is a geometric sequence

Elaborate

Each year's value is the previous year's multiplied by the common ratio $1 + r$. The simple-interest column is an arithmetic sequence with common difference $Pr$.

Nominal and effective rates

Explain

A nominal 6% compounded monthly gives an effective rate of

\left(1+\frac{0.06}{12}\right)^{12}-1 \approx 6.17\%

Discuss in class

In which year does the compound value first exceed the simple-interest value by more than ₱1,000?
Describe the two columns as sequences. Which is arithmetic? Which is geometric?
Credit cards charge about 3% per month. What effective annual rate is that? Why is it dangerous?

Problems

5 problems · check your answer, then open the solution

Problem 1 Basic

Find the maturity value of ₱15,000 invested at 5% per year compounded annually for 3 years.

Your answer (₱)
Show step-by-step solution
1. $A = P(1+r)^t = 15{,}000(1.05)^3$ .
2. $(1.05)^3 = 1.157625$ .
3. $A = 15{,}000 \times 1.157625 = 17{,}364.38$ pesos.
Answer: 17364.38 ₱
Problem 2 Standard

₱20,000 is invested at 8% per year compounded quarterly for 2 years. Find the maturity value to the nearest centavo.

Your answer (₱)
Show step-by-step solution
1. Quarterly rate $i = 0.08/4 = 0.02$ ; number of periods $n = 2 \times 4 = 8$ .
2. $A = 20{,}000(1.02)^8 \approx 20{,}000 \times 1.171659$ .
3. $A \approx 23{,}433.19$ pesos.
Answer: 23433.19 ₱
Problem 3 Basic

Two accounts both advertise 6% per year. Account X compounds annually; Account Y compounds monthly. After one year, which is true?

Choices a. X earns more b. Y earns more c. They earn exactly the same d. It depends on the deposit size
Show step-by-step solution
1. Monthly compounding adds interest on interest within the year: $(1+0.06/12)^{12} \approx 1.0617 > 1.06$ .
2. The effective rate of Y is about 6.17%, so Y earns more for any deposit.
Answer: b
Problem 4 Standard

Parents want ₱50,000 for enrolment in 5 years. How much must they deposit now at 4% compounded annually? Round to the nearest peso.

Your answer (₱)
Show step-by-step solution
1. Present value $P = \dfrac{A}{(1+r)^t} = \dfrac{50{,}000}{(1.04)^5}$ .
2. $(1.04)^5 \approx 1.216653$ .
3. $P \approx 41{,}096$ pesos.
Answer: 41096 ₱
Problem 5 Challenge Non-routine

An investment grew from ₱10,000 to ₱12,000 in 3 years with annual compounding. Find the annual rate, in percent, to two decimal places.

Your answer (%)
Show step-by-step solution
1. $12{,}000 = 10{,}000(1+r)^3 \Rightarrow (1+r)^3 = 1.2$ .
2. $1 + r = 1.2^{1/3} \approx 1.0627$ .
3. $r \approx 0.0627 = 6.27\%$ .
Answer: 6.27 %

Compound interest calculator More practice: Compound Interest More practice: Sequences in Finance