Phillip Lent $ \$1,000 $ To A Friend For $ 2 \frac{1}{2} $ Years At A Simple Interest Rate Of $ 7\% $ Per Year. How Much Was Repaid After Two And A Half Years?\[\begin{array}{l}P = \$1,000 \\t = 2.5 \\r = 0.07 \\I =
Understanding the Problem
Phillip lent $1,000 to a friend for 2.5 years at a simple interest rate of 7% per year. To calculate the amount repaid after two and a half years, we need to determine the interest accrued during this period. In this article, we will explore the concept of simple interest, calculate the interest earned, and find the total amount repaid.
What is Simple Interest?
Simple interest is a type of interest calculated only on the initial principal amount. It is calculated as a percentage of the principal amount, multiplied by the time period. The formula for simple interest is:
I = P × r × t
Where:
- I = interest
- P = principal amount (initial loan amount)
- r = interest rate (as a decimal)
- t = time period (in years)
Calculating the Interest
In this case, the principal amount (P) is $1,000, the interest rate (r) is 7% or 0.07 as a decimal, and the time period (t) is 2.5 years. Plugging these values into the simple interest formula, we get:
I = $1,000 × 0.07 × 2.5 I = $175
Total Amount Repaid
To find the total amount repaid, we need to add the interest earned to the principal amount. The principal amount is $1,000, and the interest earned is $175. Therefore, the total amount repaid is:
Total Amount Repaid = Principal Amount + Interest Earned = $1,000 + $175 = $1,175
Conclusion
In this article, we calculated the interest earned on a $1,000 loan at a 7% simple interest rate for 2.5 years. We then found the total amount repaid by adding the interest earned to the principal amount. The total amount repaid is $1,175. This calculation demonstrates the concept of simple interest and how it can be used to determine the amount repaid on a loan.
Real-World Applications
Understanding simple interest is crucial in various real-world scenarios, such as:
- Calculating interest on loans and credit cards
- Determining the return on investment (ROI) for investments
- Understanding the impact of interest rates on savings accounts and certificates of deposit (CDs)
By grasping the concept of simple interest, individuals can make informed decisions about their financial transactions and investments.
Common Mistakes to Avoid
When calculating simple interest, it's essential to avoid common mistakes, such as:
- Confusing simple interest with compound interest
- Failing to convert the interest rate to a decimal
- Misunderstanding the time period (e.g., using years instead of months or days)
By being aware of these potential pitfalls, individuals can ensure accurate calculations and make informed decisions about their financial transactions.
Additional Resources
For further learning and practice, consider the following resources:
- Online calculators for simple interest
- Financial textbooks and online courses
- Real-world examples and case studies
By exploring these resources, individuals can deepen their understanding of simple interest and apply it to various financial scenarios.
Final Thoughts
Frequently Asked Questions
In this article, we will address some common questions related to Phillip's loan repayment and simple interest calculations.
Q: What is the difference between simple interest and compound interest?
A: Simple interest is calculated only on the initial principal amount, whereas compound interest is calculated on both the principal amount and any accrued interest. This means that compound interest can result in a higher total amount repaid over time.
Q: How do I calculate compound interest?
A: The formula for compound interest is:
A = P × (1 + r)^t
Where:
- A = total amount after t years
- P = principal amount
- r = interest rate (as a decimal)
- t = time period (in years)
Q: Can I use a calculator to calculate simple interest?
A: Yes, you can use a calculator to calculate simple interest. Most calculators have a built-in function for calculating interest, or you can use the formula I = P × r × t.
Q: What if I want to calculate the interest rate instead of the interest earned?
A: To calculate the interest rate, you can rearrange the simple interest formula to solve for r:
r = I / (P × t)
Q: How do I handle partial years in simple interest calculations?
A: When dealing with partial years, you can use the following formula to calculate the interest earned:
I = P × r × (t/12)
Where:
- t/12 = the number of months in the partial year
Q: Can I use simple interest to calculate the return on investment (ROI)?
A: Yes, you can use simple interest to calculate the ROI. The ROI is the return on investment, expressed as a percentage. To calculate the ROI, you can use the following formula:
ROI = (I / P) × 100
Where:
- I = interest earned
- P = principal amount
Q: What if I want to calculate the total amount repaid on a loan with multiple payments?
A: To calculate the total amount repaid on a loan with multiple payments, you can use the following formula:
Total Amount Repaid = P + (P × r × (t1 + t2 + ... + tn))
Where:
- P = principal amount
- r = interest rate (as a decimal)
- t1, t2, ..., tn = the time periods for each payment
Conclusion
In this article, we addressed some common questions related to Phillip's loan repayment and simple interest calculations. By understanding the concept of simple interest and applying the formulas, individuals can make informed decisions about their financial transactions and investments.
Additional Resources
For further learning and practice, consider the following resources:
- Online calculators for simple interest and compound interest
- Financial textbooks and online courses
- Real-world examples and case studies
By exploring these resources, individuals can deepen their understanding of simple interest and apply it to various financial scenarios.
Final Thoughts
In conclusion, simple interest is a fundamental concept in finance that can be used to calculate the interest earned on a loan or investment. By understanding the formulas and avoiding common mistakes, individuals can make informed decisions about their financial transactions and investments.