Rigoberto invests $7,500, at 10% interest, compounded semiannually for 1 year. Use the compound interest formula to calculate the compound interest for his investment. O $750.00 O $768.75 O $8,250.00 O $8,268.75
Rigoberto invests $7,500, at 10% interest, compounded semiannually for 1 year. Use the compound interest formula to calculate the compound interest for his investment. O $750.00 O $768.75 O $8,250.00 O $8,268.75
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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Question
![### Compound Interest Calculation Problem
**Scenario:**
Rigoberto invests $7,500 at an interest rate of 10%, compounded semiannually for 1 year. Use the compound interest formula to calculate the compound interest for his investment.
**Options:**
- $750.00
- $768.75
- $8,250.00
- $8,268.75
**Explanation:**
To solve this problem, use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($7,500).
- \( r \) is the annual interest rate (decimal) (0.10).
- \( n \) is the number of times that interest is compounded per year (2 for semiannually).
- \( t \) is the time in years (1 year).
Plug in the values:
\[ A = 7500 \left(1 + \frac{0.10}{2}\right)^{2 \times 1} \]
\[ A = 7500 \left(1 + 0.05\right)^{2} \]
\[ A = 7500 \times (1.05)^2 \]
\[ A = 7500 \times 1.1025 \]
\[ A = 8,268.75 \]
The correct answer is **$8,268.75**.
**Conclusion:**
Rigoberto’s investment of $7,500 at 10% interest compounded semiannually for 1 year results in a total amount of **$8,268.75**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddf5589e-d92b-42b2-8ea5-90a454d595c8%2F7bf9414b-081e-40ec-ac96-51cb9980d39c%2Furo2yxg_processed.png&w=3840&q=75)
Transcribed Image Text:### Compound Interest Calculation Problem
**Scenario:**
Rigoberto invests $7,500 at an interest rate of 10%, compounded semiannually for 1 year. Use the compound interest formula to calculate the compound interest for his investment.
**Options:**
- $750.00
- $768.75
- $8,250.00
- $8,268.75
**Explanation:**
To solve this problem, use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($7,500).
- \( r \) is the annual interest rate (decimal) (0.10).
- \( n \) is the number of times that interest is compounded per year (2 for semiannually).
- \( t \) is the time in years (1 year).
Plug in the values:
\[ A = 7500 \left(1 + \frac{0.10}{2}\right)^{2 \times 1} \]
\[ A = 7500 \left(1 + 0.05\right)^{2} \]
\[ A = 7500 \times (1.05)^2 \]
\[ A = 7500 \times 1.1025 \]
\[ A = 8,268.75 \]
The correct answer is **$8,268.75**.
**Conclusion:**
Rigoberto’s investment of $7,500 at 10% interest compounded semiannually for 1 year results in a total amount of **$8,268.75**.
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