Compound Interest (Compounded Annually)

Abstraction: The Essence of Compound Interest

Unlocking the Potential of Compound Interest

Prepare to be amazed! In this lesson, we'll explore compound interest, a powerful concept that can significantly accelerate your financial growth. Unlike simple interest, compound interest earns interest on interest, leading to exponential growth over time.
Get ready to:

Compute compound interest, maturity value, and present value using the relevant formulas.
Solve real-world problems involving compound interest, discovering its impact on investments and loans.

By the end of this lesson, you'll understand why compound interest is often called the "miracle of compounding" and how it can work to your advantage in building wealth. Let's unlock its potential!

Activity: The Power of Compounding

Scenario: You have ₱10,000 to invest. You have two options:

Option A: A savings account offering 4% simple interest per year.

Option B: An investment account offering 4% interest compounded annually.

Calculate the total amount you would have in each option after 5 years.
Calculate the total interest earned in each option after 5 years.

Analysis: Unlocking Exponential Growth

Compare the results of the two investment options. Which option yielded a higher return? Why?

This lesson dives into the exciting world of compound interest, where your money grows exponentially. Let's explore the key concepts and formulas!

Abstraction: The Essence of Compound Interest

Compound interest is like earning interest on your interest. Each time interest is calculated, it's added to the principal, and the next period's interest is calculated on the new, larger principal. This compounding effect leads to significant growth over time.

Formula for Maturity Value

The formula for calculating the maturity value (F) of an investment with compound interest is:

Where:

F = Maturity Value
P = Principal (initial investment)
r = Interest rate per compounding period (annual rate in this case)
t = Number of compounding periods (years in this case)

Calculating Compound Interest:

Once you've calculated the maturity value (F), you can find the compound interest earned using:

Example 1: Finding Maturity Value and Compound Interest

Problem: Find the maturity value and compound interest if P10,000 is compounded annually at an interest rate of 2% for 5 years.

Solution:

P = P10,000
r = 0.02 (2% expressed as a decimal)
t = 5 years

F = P(1 + r)^t = 10,000(1 + 0.02)^5 = P11,040.81

Ic = F - P = P11,040.81 - P10,000 = P1,040.81

Therefore, the maturity value after 5 years is P11,040.81, and the compound interest earned is P1,040.81.

Formula for Present Value

To determine the present value (P) required to reach a specific future value (F) with compound interest, we use:

Finding Present Value

Problem: What is the present value of P50,000 due in 7 years if the interest rate is 10% compounded annually?

Solution:

F = P50,000
r = 0.10 (10% expressed as a decimal)
t = 7 years

P = F / (1 + r)^t = 50,000 / (1 + 0.10)^7 = P25,657.91

Therefore, the present value that needs to be invested today is P25,657.91 to accumulate to P50,000 in 7 years.

Compounding frequency can make a big difference! Here's a video lesson to understand more about how it impacts your returns.

Let's dive into the world of compound interest! This assessment evaluates your ability to calculate interest, maturity value, and present value when interest is compounded annually.

Application

Instruction: Use online resources, critical thinking, and the provided information to answer the following questions. Justify your answers with explanations and calculations. Upload your documents on this google drive link: Module 1 Lesson 3 Activity Outputs

(Note: Make sure your file name will be your Section-Year-Surname-Given_Name-Module#-Lesson#-Output#, for example: [GAS11-DelaCruz-Juan-Module1-Lesson1-Output1]. Wrong file name will subject to score deduction.)

Scenario 1: Investing for the Future

You receive a gift of ₱10,000 and decide to invest it for 5 years at a 2% annual interest rate compounded annually.

Inquiry Questions:

Calculate the maturity value of your investment after 5 years. Use the formula F = P(1 + r)^t.
How much interest will you earn over the 5-year period? Calculate the compound interest using Ic = F - P.
Compare this result with the simple interest earned on the same principal, rate, and time. What is the key difference between the growth of simple and compound interest?
If the interest rate increased to 3%, how would this affect the maturity value? Recalculate the maturity value with the new interest rate and analyze the impact.

Scenario 2: Planning for a Large Purchase

You want to have ₱200,000 in 6 years to make a down payment on a house. You find a bank offering a time deposit with a 1.1% annual interest rate compounded annually.

Inquiry Questions:

How much money do you need to deposit now to reach your goal in 6 years? Use the present value formula: P = F(1 + r)^-t.
If you could find a time deposit with a 1.5% interest rate, how much less would you need to deposit initially? Recalculate the present value with the new interest rate and compare the difference.
Research different investment options available for long-term savings goals. Compare interest rates, risks, and potential returns. What factors should you consider when choosing a long-term investment?

Scenario 3: Analyzing Investment Opportunities

You are presented with two investment options:

Option A: Invest ₱50,000 for 7 years at a 10% annual interest rate compounded annually.

Option B: Invest ₱50,000 for 8 years at an 8% annual interest rate compounded annually.

Inquiry Questions:

Calculate the maturity value for both investment options.
Which option yields a higher return? Analyze the results and explain your reasoning.
What are the advantages and disadvantages of each option? Consider factors like the time horizon and the potential return.
If you needed the money sooner than the specified time frame, how would this affect your decision?

Compound interest making sense? Let's explore more complex scenarios in Lesson 4!

Lesson 4: Compound Interest: Compounding More Than Once a Year

Page updated

Google Sites

Report abuse