4th-PPTECON123

Overview

  • Presentation from Manuel S. Enverga University Foundation, focused on Engineering Economy (ECON123).

Interest

  • Definition: Interest is the money paid for the use of borrowed capital. It serves as income for the lender.

  • Classification:

    • Simple Interest

    • Compound Interest

Simple Interest

  • Formula: I = P x R x T

    • I = Interest

    • P = Principal Amount

    • R = Rate of Interest

    • T = Time (in years)

  • Concept: Simple interest is directly proportional to the principal and time.

Future Value with Simple Interest

  • Formula: F = P + I = P(1 + RT)

  • Interpretation: Total amount to be repaid is the principal plus total interest.

Time Calculation

  • Ordinary Time: Assumes 30 days per month (360 days/year).

  • Exact Time: Counts the exact number of days (365 for regular years, 366 for leap years).

Ordinary and Exact Interest

  • Ordinary Interest: Computed on a banker’s year (360 days).

  • Exact Interest: Based on the actual number of days counted.

Compound Interest

  • Definition: Interest where the principal earns interest over multiple periods; the interest is added to the principal for future interest calculations.

  • Formulas:

    • F = P(1 + r)^n

    • F = P(1 + r/m)^(mn)

  • Key Concept: Interest is calculated on accumulated interest as well as the principal.

Nominal & Effective Rate of Interest

  • Nominal Rate: The interest rate before adjustments for inflation or compounding effects (i = r x m).

  • Effective Rate: Takes into account the effect of compounding during the year.

    • Formula: i_e = (1 + i/n)^n - 1

  • Example Problem: If $500 is deposited at 6% compounded quarterly, calculate the amount after one year.

Example Problems

  • Calculate effective and nominal interest rates based on given scenarios, like a deposit at a specific compounding rate or a credit card policy.

  • Reflect on scenarios such as investment comparisons: 12% compounded monthly vs 12.5% annually to evaluate which is more favorable.

Present Value

  • Formulas:

    • P = F(1 + i)^{-n}

    • P = F(1 + i)^{n}

  • Explanation of how present value calculations are key in finance to ascertain what a future sum is worth today.

Examples

  • Ordinary Simple Interest Example: Calculate interest for a principal of P10,000 over 9 months and 10 days at 12%.

  • Ordinary vs. Exact Example: Determine the interests for specific date ranges comparing ordinary and exact time calculations.

  • Investment Growth: Show compound interest calculations for investments over multiple years, determining future values based on varying interest rates.

  • Maturity Value Calculation: Find present values of promissory notes factoring in compound interest and different compounding frequencies.

Chapter Conclusion

  • Key concepts from the lecture tie into practical applications for finance students and engineering contexts.

  • Quote for Reflection: "He who establishes his argument by noise and command shows that his reason is weak." - Michel de Montaigne

Quiz Questions

  • Practice problems focusing on concepts of interest calculation, including future value, present value, ordinary and exact time, and comparisons between investment options.

  • These exercises reinforce the understanding of interest mathematics in real-world scenarios.