General Mathematics Quiz on Interest Formulas

Simple Interest

• Formula: ( I = P \times r \times t )
  • Where ( I ) is interest, ( P ) is principal, ( r ) is rate (as a decimal), and ( t ) is time in years.
• Example: Investing Php 1,000 at 5% annually earns Php 100 in 2 years.
• Interest increases with a longer time period.

Compound Interest

• Formula: ( A = P(1 + \frac{r}{k})^{kt} )
  • ( A ) is the future amount, ( k ) is the frequency of compounding per year.
• Compound interest is calculated on the principal and previously earned interest.
• Higher compounding frequency results in greater interest earnings.
• Example: Investing Php 1,000 at 5% compounded annually results in Php 1,102.50 after 2 years.
• Example: Php 2,500 compounded semi-annually at 6% for 3 years yields Php 2,760.00.

Interest Rates and Duration

• Simple interest is straightforward, while compound interest can yield significantly more depending on compounding frequency.
• For high-frequency compounding scenarios, compound interest generally provides superior returns compared to simple interest.
• Interest earned in simple interest and compound interest correlates directly with time and frequency.

Principal Amount Calculation

• For calculating principal with future amount, use:
  • ( P = \frac{A}{(1 + r \times t)} ) for simple interest.
• Example: For a future amount of Php 3,000 at 6% over 2 years, the principal is Php 2,800.

Common Misconceptions

• Simple interest is not always greater than compound interest for the same conditions.
• Time periods for calculating simple interest must be in years.
• More frequent compounding increases the total interest earned.
• Not only principal, rate, and time influence interest; compounding frequency also plays a vital role.