Elizabeth Loishorwa
4 hours ago
What are the difference between simple and compound interest?
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ChatGPT
4 hours ago
Simple interest is calculated only on the principal amount of a loan or investment, while compound interest is calculated on both the principal amount and any accumulated interest from previous periods.
Simple interest is linear, meaning the amount of interest earned or paid remains constant over time, while compound interest grows exponentially as interest is added to the principal amount.
In simple interest, the formula is:
Interest = Principal x Rate x Time
In compound interest, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan
P = the principal amount
r = the annual interest rate
n = the number of times interest is compounded per year
t = the number of years
Overall, compound interest results in higher returns or higher costs compared to simple interest over time due to the compounding effect.
Simple interest is linear, meaning the amount of interest earned or paid remains constant over time, while compound interest grows exponentially as interest is added to the principal amount.
In simple interest, the formula is:
Interest = Principal x Rate x Time
In compound interest, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan
P = the principal amount
r = the annual interest rate
n = the number of times interest is compounded per year
t = the number of years
Overall, compound interest results in higher returns or higher costs compared to simple interest over time due to the compounding effect.
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Google Gemini AI
4 hours ago
Simple Interest
- Calculated on the principal amount only
- Same interest rate is applied throughout the term of the loan or investment
- Formula: I = P - r - t
- I = interest
- P = principal
- r = annual interest rate as a decimal
- t = time (in years)
Compound Interest
- Calculated on the principal plus any accumulated interest
- Interest rate is applied to the growing balance
- Formula: A = P - (1 + r)^nt
- A = final amount, including principal and interest
- P = principal
- r = annual interest rate as a decimal
- n = number of compounding periods per year
- t = time (in years)
Key Differences
- Basis of Calculation: Simple interest is calculated on the initial principal amount only, while compound interest is calculated on the growing balance.
- Growth Rate: Compound interest grows faster than simple interest, especially over longer periods.
- Impact of Time: The longer the term of the loan or investment, the greater the difference between simple and compound interest.
- Flexibility: Compound interest is more flexible, as it allows for more frequent compounding. This can lead to a higher final amount.
Example
Consider a loan of $1,000 for 5 years at an interest rate of 5%.
- Simple Interest: Interest = $1,000 - 0.05 - 5 = $250. Total amount: $1,000 (principal) + $250 (interest) = $1,250.
- Compound Interest (annual compounding): Amount = $1,000 - (1 + 0.05)^5 = $1,338.23.
As you can see, compound interest results in a higher final amount.
- Calculated on the principal amount only
- Same interest rate is applied throughout the term of the loan or investment
- Formula: I = P - r - t
- I = interest
- P = principal
- r = annual interest rate as a decimal
- t = time (in years)
Compound Interest
- Calculated on the principal plus any accumulated interest
- Interest rate is applied to the growing balance
- Formula: A = P - (1 + r)^nt
- A = final amount, including principal and interest
- P = principal
- r = annual interest rate as a decimal
- n = number of compounding periods per year
- t = time (in years)
Key Differences
- Basis of Calculation: Simple interest is calculated on the initial principal amount only, while compound interest is calculated on the growing balance.
- Growth Rate: Compound interest grows faster than simple interest, especially over longer periods.
- Impact of Time: The longer the term of the loan or investment, the greater the difference between simple and compound interest.
- Flexibility: Compound interest is more flexible, as it allows for more frequent compounding. This can lead to a higher final amount.
Example
Consider a loan of $1,000 for 5 years at an interest rate of 5%.
- Simple Interest: Interest = $1,000 - 0.05 - 5 = $250. Total amount: $1,000 (principal) + $250 (interest) = $1,250.
- Compound Interest (annual compounding): Amount = $1,000 - (1 + 0.05)^5 = $1,338.23.
As you can see, compound interest results in a higher final amount.
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