Simple-Interest

Simple Interest Overview

Simple interest is the amount paid on top of a principal loan or investment over a specified period. It involves the original amount borrowed or invested, the interest rate applied, and the time period involved.

Learning Objectives

At the end of this lesson, learners should be able to:

• Correctly compute for simple interest.

• Solve word problems involving simple interest.

Key Concepts

Interest

• Interest refers to the additional amount that can be earned or paid on top of the principal amount.

• Example: If someone borrows ₱10,000 at a 2% simple interest rate, the interest earned after one year would be ₱200, computed as 2% of ₱10,000.

Lender and Borrower

• Lender (Creditor): The party providing the money or extending credit.

• Borrower (Debtor): The party receiving and using the money or credit.

Principal

• The principal is the original sum of money extended for credit or deposited in a bank.

• Example: For a loan of ₱10,000 at 2% interest, the principal is ₱10,000.

Interest Rate

• The interest rate is the percent charged for using the principal over a specific time, expressed as a percentage or decimal.

• Example: In a loan of ₱10,000 at 2%, the interest rate is 2%.

Time of Interest

• This refers to the duration for which the money is borrowed until the due date of payment.

• Example: Again, for the ₱10,000 loan at 2% interest, the time of interest is one year.

Maturity Date

• The maturity date is the deadline for the payment of the principal plus interest.

Simple Interest Definition

• Simple interest is calculated only on the original principal amount during the entire loan period.

Formula for Simple Interest

• The formula for calculating simple interest is given by

  [ I = P \times r \times t ]

Where:

• ( I ) = Interest amount

• ( P ) = Principal

• ( r ) = Simple interest rate (in decimal)

• ( t ) = Time in years

Example Problems

Example 1

• Problem: Anthony borrows ₱100,000 at a 4% interest rate for 2 years.

• Solution:

  • Principal (P) = ₱100,000

  • Interest rate (r) = 4% = 0.04

  • Time (t) = 2 years

  • Calculation: ( I = 100,000 \cdot 0.04 \cdot 2 = ₱8,000 )

  • Total Interest: Tony pays ₱8,000 after 2 years.

Example 2

• Problem: Steve invests ₱150,000 with a 6% interest rate for 9 months.

Practice Problems

1. Calculate interest for ₱60,000 at 6% after 3 years.

2. Total interest owed by Scott for a ₱100,000 loan at 7.2% for 2 years.

3. Maturity value of ₱25,000 savings at 5.25% after 3 years.

4. Calculate total payment by Peggy for a ₱200,000 loan at 8% after 10 months.

5. Total payment for a ₱100,000 loan at 12% after 2 years.