SIMPLE AND COMPOUND INTEREST

SIMPLE AND COMPOUND INTEREST

  • By Ms. Rezi U. Lodriga

Objectives

  • Illustrate simple and compound interests

  • Distinguish between simple and compound interests

  • Compute interest, maturity value, future value, and present value

  • Solve problems involving simple and compound interests

Key Concepts

Simple Interest

  • Formula: I = P x r x t

    • P: Principal

    • r: Annual simple interest rate

    • t: Time in years

Principal and Values

  • Principal: Original amount of money invested, saved, or loaned

  • Future Value (F): Accumulated value including all interest earned

  • Present Value (PV): Amount needed now to accumulate a future value

Interest

  • Interest is the difference between the amount returned and the amount borrowed.

Simple vs. Compound Interest

  • Simple Interest: Earned only on the principal

  • Compound Interest: Earned on both the principal and previously earned interest

Calculation Examples

  • Example of Simple Interest:

    • If P = 100,000, r = 10% compounded annually, compute for 3 years

  • Compound Interest leads to higher returns than Simple Interest due to the accumulation of interest on interest.

Computation Techniques

Future Value Formula

  • F = P(1 + rt)

Present Value Formula

  • P = F (1 + rt)

Continuous Compounding

  • Future value formula for continuous compounding: A = Pe^(rt)

  • Where e ≈ 2.7182818

Practical Applications

  • Importance of considering interest rates before borrowing or lending money

Guide Questions

  • Considerations before lending money

  • Steps to solve compounded problems

Summary of Examples

  • Ariel: Borrowed P5,000 at 5% for 2 years = Total P5,500

  • Belle: Borrowed P250,000 at 2% for 5 years = Total P275,000

  • Aurora: To save P1,450 from P1,000 at 3% = 15 years

  • Snow White’s parents need to deposit P186,046.51 to reach P200,000 in 3 years at 2.5%.