3. An amount $4,000 is invested today and another $10,000 invested four years from now. If both of them earn a simple interest of 10%, the interest accrued at the end of 5 years is?-
3. An amount $4,000 is invested today and another $10,000 invested four years from now. If both of them earn a simple interest of 10%, the interest accrued at the end of 5 years is?-
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Problem 3: Simple Interest Calculation**
An amount of $4,000 is invested today and another $10,000 is invested four years from now. If both of these investments earn a simple interest rate of 10%, what is the total interest accrued at the end of 5 years?
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**Solution Explanation:**
To solve this, we will calculate the simple interest for each investment separately and then sum them up.
**Step 1: Calculate the interest for the $4,000 investment:**
- **Principal (P)**: $4,000
- **Time (T)**: 5 years (because it is invested today)
- **Rate (R)**: 10% per annum
Simple Interest (SI) = \( \frac{P \times R \times T}{100} \)
\[ \text{SI} = \frac{4000 \times 10 \times 5}{100} = 2000 \]
The interest accrued on the $4,000 in 5 years is $2,000.
**Step 2: Calculate the interest for the $10,000 investment:**
- **Principal (P)**: $10,000
- **Time (T)**: 1 year (because it is invested 4 years from now, so only 1 year left for it to earn interest)
- **Rate (R)**: 10% per annum
Simple Interest (SI) = \( \frac{P \times R \times T}{100} \)
\[ \text{SI} = \frac{10000 \times 10 \times 1}{100} = 1000 \]
The interest accrued on the $10,000 in 1 year is $1,000.
**Total Interest Calculation:**
Total Interest = Interest from $4,000 + Interest from $10,000
Total Interest = $2,000 + $1,000 = $3,000
Thus, the total interest accrued at the end of 5 years is $3,000.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09b3997c-2096-4573-b74b-055c69181c0d%2Fc08bcf16-248a-47fd-bd7e-727d53c3d117%2Fwgi5n9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 3: Simple Interest Calculation**
An amount of $4,000 is invested today and another $10,000 is invested four years from now. If both of these investments earn a simple interest rate of 10%, what is the total interest accrued at the end of 5 years?
---
**Solution Explanation:**
To solve this, we will calculate the simple interest for each investment separately and then sum them up.
**Step 1: Calculate the interest for the $4,000 investment:**
- **Principal (P)**: $4,000
- **Time (T)**: 5 years (because it is invested today)
- **Rate (R)**: 10% per annum
Simple Interest (SI) = \( \frac{P \times R \times T}{100} \)
\[ \text{SI} = \frac{4000 \times 10 \times 5}{100} = 2000 \]
The interest accrued on the $4,000 in 5 years is $2,000.
**Step 2: Calculate the interest for the $10,000 investment:**
- **Principal (P)**: $10,000
- **Time (T)**: 1 year (because it is invested 4 years from now, so only 1 year left for it to earn interest)
- **Rate (R)**: 10% per annum
Simple Interest (SI) = \( \frac{P \times R \times T}{100} \)
\[ \text{SI} = \frac{10000 \times 10 \times 1}{100} = 1000 \]
The interest accrued on the $10,000 in 1 year is $1,000.
**Total Interest Calculation:**
Total Interest = Interest from $4,000 + Interest from $10,000
Total Interest = $2,000 + $1,000 = $3,000
Thus, the total interest accrued at the end of 5 years is $3,000.
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