4-4 Staci invested $950 five years ago. Her investment paid 7.2 percent interest compounded monthly. Staci's twin sister Shelli invested $900 at the same time. But Shelli's investment earned 8 percent interest compounded quarterly. How much is each investment worth today?
4-4 Staci invested $950 five years ago. Her investment paid 7.2 percent interest compounded monthly. Staci's twin sister Shelli invested $900 at the same time. But Shelli's investment earned 8 percent interest compounded quarterly. How much is each investment worth today?
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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I came up with this Shelly $1,360.1990 her sister $1,335.6312, is my answer correct
![### Financial Mathematics Example: Compound Interest Calculation
**Scenario:**
Staci invested $950 five years ago. Her investment earned 7.2 percent interest compounded monthly. Staci's twin sister, Shelli, invested $900 at the same time. Shelli's investment earned 8 percent interest compounded quarterly. We are to determine the current value of each investment.
**Key Details:**
- **Staci's Investment:**
- Principal: $950
- Annual interest rate: 7.2% (compounded monthly)
- Time: 5 years
- **Shelli's Investment:**
- Principal: $900
- Annual interest rate: 8% (compounded quarterly)
- Time: 5 years
**Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial sum of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
**Solutions:**
1. **Staci's Investment Calculation:**
\[ P = 950 \]
\[ r = 0.072 \]
\[ n = 12 \] (monthly compounding)
\[ t = 5 \]
\[ A = 950 \left(1 + \frac{0.072}{12}\right)^{12 \times 5} \]
\[ A \approx 950 \left(1 + 0.006\right)^{60} \]
\[ A \approx 950 (1.006)^{60} \]
\[ A \approx 950 \times 1.432364 \]
\[ A \approx 1360.75 \]
So, Staci’s investment is worth approximately $1360.75 today.
2. **Shelli's Investment Calculation:**
\[ P = 900 \]
\[ r = 0.08 \]
\[ n = 4 \] (quarterly compounding)
\[ t = 5 \]
\[ A = 900 \left(1 + \frac{0.08}{4}\right)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc46bd967-cfaf-4c01-b215-18f93da41394%2F38bde347-6ec1-4cfe-a4f7-09044daec36e%2Fliiqh3_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Financial Mathematics Example: Compound Interest Calculation
**Scenario:**
Staci invested $950 five years ago. Her investment earned 7.2 percent interest compounded monthly. Staci's twin sister, Shelli, invested $900 at the same time. Shelli's investment earned 8 percent interest compounded quarterly. We are to determine the current value of each investment.
**Key Details:**
- **Staci's Investment:**
- Principal: $950
- Annual interest rate: 7.2% (compounded monthly)
- Time: 5 years
- **Shelli's Investment:**
- Principal: $900
- Annual interest rate: 8% (compounded quarterly)
- Time: 5 years
**Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial sum of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
**Solutions:**
1. **Staci's Investment Calculation:**
\[ P = 950 \]
\[ r = 0.072 \]
\[ n = 12 \] (monthly compounding)
\[ t = 5 \]
\[ A = 950 \left(1 + \frac{0.072}{12}\right)^{12 \times 5} \]
\[ A \approx 950 \left(1 + 0.006\right)^{60} \]
\[ A \approx 950 (1.006)^{60} \]
\[ A \approx 950 \times 1.432364 \]
\[ A \approx 1360.75 \]
So, Staci’s investment is worth approximately $1360.75 today.
2. **Shelli's Investment Calculation:**
\[ P = 900 \]
\[ r = 0.08 \]
\[ n = 4 \] (quarterly compounding)
\[ t = 5 \]
\[ A = 900 \left(1 + \frac{0.08}{4}\right)
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