Questions and Answers
What is the formula for calculating simple interest?
What happens to the future value of an investment if the frequency of compounding increases?
How much interest will you earn if you invest Php 1,000 at an annual interest rate of 4% compounded quarterly for one year?
In what scenario does compound interest result in greater earnings compared to simple interest?
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What is the future amount of a Php 2,500 investment at a 6% annual interest rate compounded semi-annually for three years?
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If you invest Php 1,000 at an annual interest rate of 5% compounded annually, how much will you have after two years?
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What is the principal amount if the future amount is Php 3,000, the interest rate is 6%, and the time period is 2 years for simple interest?
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What is the formula for calculating the future amount in compound interest?
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Study Notes
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.
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Description
Test your knowledge on the formulas for calculating simple and compound interest with this General Mathematics quiz. You'll answer questions on key concepts and calculations essential for understanding interest rates. Challenge yourself to see how well you grasp these financial principles!
