Finance: Simple vs Compound Interest

Simple Interest

• Simple interest is calculated only on the principal amount.
• It doesn't consider the interest earned in previous periods.
• Formula: Simple Interest = (Principal × Rate × Time) / 100
• Where:
  • Principal = the initial amount of money.
  • Rate = the annual interest rate (as a percentage).
  • Time = the duration of the investment in years.
• Simple interest is straightforward to calculate, but it's generally less lucrative than compound interest for long-term investments.

Compound Interest

• Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods.
• It's calculated more frequently than simple interest, usually daily, monthly, quarterly, semi-annually, or annually.
• The formula for compound interest is more complicated and can be based on different frequencies. (This is different from simple interest, which is only calculated once at the end of the investment period.)
• Compound interest leads to faster growth of an investment compared to simple interest, over time. This is because of the compounding effect, where the interest earned also earns interest.
• The formula for compound interest is: A = P(1 + r/n)^(nt)
  • Where:
    • A = the future value of the investment/loan, including interest.
    • P = the principal investment amount (the initial deposit or loan amount).
    • r = the annual interest rate (decimal).
    • n = the number of times that interest is compounded per year.
    • t = the number of years the money is invested or borrowed for.

Semi-Annual Interest

• Interest that is compounded every six months.
• In this case, n = 2 in the compound interest formula.
• This results in interest being calculated twice a year, leading to a higher return compared to annual compounding for the same rate and time period.

Monthly Interest

• Interest that is compounded every month.
• This results in interest being calculated 12 times a year, leading to a higher return compared to annual compounding for a given rate and time period.
• In this calculation, n = 12 in the compound interest formula.

Compounded Quarterly Interest

• Interest that is compounded every three months.
• Results in interest being calculated 4 times a year.
• Leading to a higher return compared to annual compounding for the same rate and time period.
• In this calculation, n = 4 in the compound interest formula.

Compounded Continuously Interest

• Interest that is compounded continuously, meaning the interest is calculated and added to the principal continuously.
• The most frequent compounding, resulting in the highest potential return for a given rate and period.
• This is a special case of compound interest and is calculated utilizing calculus techniques.
• The formula for continuously compounded interest is: A = Pe^(rt)
  • Where:
    • e = the mathematical constant approximately equal to 2.71828.

This quiz explores the concepts of simple and compound interest, including their formulas and applications. Understand how each type of interest works and their implications for investments. Test your knowledge on calculating both simple and compound interests effectively.