Simple and Compound Interest Problems Explained | Algebra 2
your math tutor・2 minutes read
Simple interest is calculated using the formula \( i = p \times r \times t \), while compound interest accumulates on the total amount, including previously earned interest. For example, a $1,000 deposit at a 6% interest rate results in different amounts after a year: $60 with simple interest versus $1,061.68 with compound interest, highlighting the significantly faster growth of compound interest.
Insights
- Simple interest is straightforward and calculated using the formula \( i = p \times r \times t \), which shows how much interest is earned or paid based on the principal, interest rate, and time. For example, a $1,000 deposit at a 6% interest rate earns $60 in one year, highlighting the significant difference in earnings or costs depending on the interest rate applied.
- In contrast, compound interest builds on itself by calculating interest on both the principal and any previously earned interest, leading to greater returns or costs over time. For instance, a $1,000 deposit at a 6% interest rate compounded monthly results in $1,061.68 after one year, compared to just $1,060 with simple interest, demonstrating how compound interest can significantly increase the total amount owed, especially in cases like credit card debt, where high rates can lead to rapid accumulation of costs.
Get key ideas from YouTube videos. It’s free
Recent questions
What is simple interest?
Simple interest is a method of calculating the interest on a principal amount over a specific period of time at a fixed interest rate. It is determined using the formula \( i = p \times r \times t \), where \( i \) represents the interest earned, \( p \) is the principal amount, \( r \) is the interest rate expressed in decimal form, and \( t \) is the time in years. For example, if you deposit $1,000 at an interest rate of 6% for one year, the interest earned would be $60. This straightforward calculation makes simple interest easy to understand and apply, especially for short-term loans or investments.
How is compound interest calculated?
Compound interest is calculated by applying interest to the initial principal as well as to the accumulated interest from previous periods. The formula used for calculating compound interest is \( A = p \times (1 + \frac{r}{n})^{n \times t} \), where \( A \) is the total amount after interest, \( p \) is the principal, \( r \) is the interest rate in decimal form, \( n \) is the number of times interest is compounded per year, and \( t \) is the number of years. For instance, if you invest $1,000 at a 6% interest rate compounded monthly, after one year, you would have approximately $1,061.68. This method allows your investment to grow at a faster rate compared to simple interest, as it takes into account the interest that has already been added to the principal.
What is the difference between simple and compound interest?
The primary difference between simple and compound interest lies in how interest is calculated and applied. Simple interest is calculated only on the principal amount throughout the investment or loan period, using the formula \( i = p \times r \times t \). In contrast, compound interest is calculated on both the principal and the accumulated interest from previous periods, leading to a potentially higher total amount over time. For example, if you invest $1,000 at a 6% interest rate, simple interest would yield $60 after one year, while compound interest would yield approximately $1,061.68 when compounded monthly. This distinction is crucial for understanding how investments grow and how loans can accumulate debt over time.
What happens with credit card debt?
Credit card debt can escalate rapidly due to the effects of compound interest, which is often applied to outstanding balances. When a charge is made on a credit card, the interest accumulates on the total amount owed, including any previously accrued interest. For example, if you have a $2,000 charge at a 15% interest rate compounded daily, after six months, the total amount owed could rise to approximately $2,155.74. This illustrates how quickly debt can accumulate if payments are not made regularly, emphasizing the importance of managing credit card usage and making timely payments to avoid excessive interest charges.
How do I calculate total repayment on a loan?
To calculate the total repayment on a loan, you can use the simple interest formula \( i = p \times r \times t \) to determine the interest amount, and then add that to the principal. For instance, if you take out a $5,000 loan at a 4% interest rate over three years, the interest would be calculated as $600. Therefore, the total repayment amount would be the sum of the principal and the interest, resulting in $5,600. This straightforward calculation helps borrowers understand their financial obligations and plan their repayments accordingly.
Related videos
Summary
00:00
Understanding Simple and Compound Interest
- Simple interest is calculated using the formula \( i = p \times r \times t \), where \( i \) is the interest earned, \( p \) is the principal amount (initial deposit), \( r \) is the interest rate in decimal form, and \( t \) is the time in years. For example, depositing $1,000 at a 6% interest rate for one year yields $60 in interest, while a more realistic rate of 0.5% results in only $5 in interest for the same period.
- When borrowing money, the same formula applies. For instance, if you take out a $5,000 loan at a 4% interest rate over three years, the interest paid would be $600, resulting in a total repayment of $5,600.
- Compound interest differs from simple interest as it calculates interest on the accumulated amount, including previously earned interest. For example, depositing $1,000 at a 6% interest rate compounded monthly results in $1,061.68 after one year, compared to $1,060 from simple interest.
- The compound interest formula is \( A = p \times (1 + \frac{r}{n})^{n \times t} \), where \( A \) is the future amount, \( p \) is the principal, \( r \) is the interest rate in decimal form, \( n \) is the number of compounding periods per year, and \( t \) is the time in years. For example, with $1,000 at 6% compounded monthly, \( n = 12 \) and \( t = 1 \), resulting in $1,061.68.
- Credit card debt can escalate quickly due to compound interest. For a $2,000 charge at a 15% interest rate compounded daily, after six months (0.5 years), the total owed would be $2,155.74, illustrating how quickly debt can accumulate if payments are not made.
