You're trying to save to buy a new $275,000 Ferrari. You have $50,000 today that can be invested at your bank. The bank pays 4.8 percent annual interest on its accounts. How long will it be before you have enough to buy the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
You're trying to save to buy a new $275,000 Ferrari. You have $50,000 today that can be invested at your bank. The bank pays 4.8 percent annual interest on its accounts. How long will it be before you have enough to buy the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
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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![### Investment Interest Calculation
**Scenario:**
- You aim to purchase a new Ferrari priced at $275,000.
- Currently, you have $50,000 available for investment.
- The bank offers an annual interest rate of 4.8% on its accounts.
**Objective:**
- Determine the number of years required to accumulate enough money to purchase the Ferrari using the given initial investment and interest rate.
**Instructions:**
1. **Calculate Using the Compound Interest Formula:**
The compound interest formula is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \(A\) is the future value of the investment/loan, including interest.
- \(P\) is the principal investment amount (initial deposit or loan amount).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per unit \(t\).
- \(t\) is the time the money is invested for in years.
2. **Given Data:**
- \(A = 275,000\)
- \(P = 50,000\)
- \(r = 4.8\% \text{ or } 0.048\)
- Assuming interest is compounded once per year (\(n = 1\))
3. **Rearrange the Formula to Solve for \(t\):**
\[
t = \frac{\log\left(\frac{A}{P}\right)}{n \cdot \log\left(1 + \frac{r}{n}\right)}
\]
4. **Perform Calculations:**
- First, substitute the values into the equation.
\[
t = \frac{\log\left(\frac{275,000}{50,000}\right)}{\log\left(1 + 0.048\right)}
\]
- Calculate the logarithms and solve for \(t\).
5. **Enter Your Answer:**
- Ensure to **not round** intermediate calculations and **round the final answer to 2 decimal places**.
Enter your result in the provided text box:
```
Number of years: [Your Answer]
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0505985e-243e-4b9e-b7a6-bbe3450b2962%2Fc4e56883-d191-4e2b-8f6e-0d1a5d309b4e%2F4cmo7e4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Investment Interest Calculation
**Scenario:**
- You aim to purchase a new Ferrari priced at $275,000.
- Currently, you have $50,000 available for investment.
- The bank offers an annual interest rate of 4.8% on its accounts.
**Objective:**
- Determine the number of years required to accumulate enough money to purchase the Ferrari using the given initial investment and interest rate.
**Instructions:**
1. **Calculate Using the Compound Interest Formula:**
The compound interest formula is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \(A\) is the future value of the investment/loan, including interest.
- \(P\) is the principal investment amount (initial deposit or loan amount).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per unit \(t\).
- \(t\) is the time the money is invested for in years.
2. **Given Data:**
- \(A = 275,000\)
- \(P = 50,000\)
- \(r = 4.8\% \text{ or } 0.048\)
- Assuming interest is compounded once per year (\(n = 1\))
3. **Rearrange the Formula to Solve for \(t\):**
\[
t = \frac{\log\left(\frac{A}{P}\right)}{n \cdot \log\left(1 + \frac{r}{n}\right)}
\]
4. **Perform Calculations:**
- First, substitute the values into the equation.
\[
t = \frac{\log\left(\frac{275,000}{50,000}\right)}{\log\left(1 + 0.048\right)}
\]
- Calculate the logarithms and solve for \(t\).
5. **Enter Your Answer:**
- Ensure to **not round** intermediate calculations and **round the final answer to 2 decimal places**.
Enter your result in the provided text box:
```
Number of years: [Your Answer]
```
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