general-mathematics-Lesson

Simple and Compound Interest

Simple Interest Formula

  • Definition: The interest earned on a principal amount at a fixed rate over a certain period.

  • Formula: Is = Prt

    • Where:

      • Is = Interest earned

      • P = Principal amount

      • r = Interest rate (as a decimal)

      • t = Time (in years)

Example 1: Simple Interest Calculation

  • Given:

    • P = ₱1,000,000

    • r = 0.25% = 0.0025

    • t = 1 year

  • Calculate: Is

    • Is = ₱1,000,000 x 0.0025 x 1 = ₱2,500

Example 2: Finding Principal Amount

  • Given:

    • r = 7% = 0.07

    • t = 2 years

    • Is = ₱11,200

  • Calculate: P

  • Formula rearranged: P = Is / (rt)

  • P = ₱11,200 / (0.07 x 2) = ₱80,000

Compound Interest

Compound Interest Formula

  • Definition: The interest calculated on the initial principal and also on the accumulated interest from previous periods.

  • Formula: F = P(1 + r)^t

    • Where:

      • F = Future value (maturity value)

      • P = Principal

      • r = Interest rate per period (as a decimal)

      • t = Number of periods

Example 3: Maturity Value Calculation

  • Given:

    • P = ₱10,000

    • r = 2% = 0.02

    • t = 5 years

  • Calculate:

    • F = ₱10,000 x (1 + 0.02)^5 = ₱11,040.81

  • Calculate Compound Interest (Ic):

    • Ic = F - P = ₱11,040.81 - ₱10,000 = ₱1,040.81

Example 4: Present Value Calculation

  • Given:

    • F = ₱50,000

    • r = 10% = 0.1

    • t = 7 years

  • Calculate: P

  • Formula rearranged: P = F / (1 + r)^t

  • P = ₱50,000 / (1 + 0.1)^7 = ₱25,657.91

Annuities

Definition of Annuity

  • Annuity: A sequence of payments made at equal (fixed) intervals.

  • Types:

    • Simple Annuity: Payment interval matches the interest period.

    • General Annuity: Payment interval does not match the interest period.

Example of Simple Annuity

  • Mrs. Remoto saves ₱3,000 monthly for 6 years at 9% compounded monthly.

    • Simple Annuity as payment and interest intervals are the same.

Example of General Annuity

  • Cris deposits ₱1,000 monthly at 6% compounded quarterly for 15 years.

    • General Annuity as payment and interest intervals differ.

Future Value Formula of Simple Annuity

  • Given by: (1 + Ā)^n - 1 / Ā

  • Where:

    • F = Future Value of a Simple Annuity

    • R = Regular Payment

    • j = Interest Rate per Period

    • n = Number of Payments

Example Calculation

  • Conceptualize based on previous examples of calculating Future Values in annuity cases.

  • Use rearranged formulas accordingly.

Deferred Anuity

  • Definition: Begins once a specified time has elapsed.

  • Formula: 1 − (1 + Ā)^(n+k) / (1 + Ā)^k * R / Ā

  • Where k signifies deferment duration.

Stocks and Bonds

Stocks

  • Definition: Represents ownership in a company.

  • Types:

    • Common Stock: Voting rights; dividends based on profits.

    • Preferred Stock: Fixed dividends; no voting rights.

Bonds

  • Definition: Debt securities promising returns at maturity.

  • Types:

    • Government Bonds: Low risk; stable returns.

    • Corporate Bonds: Higher yield but increased risk of default.

    • Zero-Coupon Bonds: No periodic interest; lump sum at maturity.

Example Problem

  1. Calculate dividend per share including given total dividend and share count.

  • Total Dividend = ₱30,000,000 / Total Shares = ₱700,000