(Related to Checkpoint 5.5) (Solving for n) Jack asked Jill to marry him, and she has accepted under one condition: Jack must buy her a new $330,000 Rolls-Royce Phantom. Jack currently has $21,600 that he may invest. He has found a mutual fund with an expected annual return of 7.5 percent in which he will place the money. How long will it take Jack to win Jill's hand in marriage? Ignore taxes and inflation. The number of years it will take for Jack to win Jill's hand in marriage is years. (Round to one decimal place.)
(Related to Checkpoint 5.5) (Solving for n) Jack asked Jill to marry him, and she has accepted under one condition: Jack must buy her a new $330,000 Rolls-Royce Phantom. Jack currently has $21,600 that he may invest. He has found a mutual fund with an expected annual return of 7.5 percent in which he will place the money. How long will it take Jack to win Jill's hand in marriage? Ignore taxes and inflation. The number of years it will take for Jack to win Jill's hand in marriage is years. (Round to one decimal place.)
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 thought 38 years was correct answer. It is not accepting in the answer box
![## Excel Formula and Data Example
### Description:
The image shows a spreadsheet in Microsoft Excel containing a formula and some numerical data. This is an educational example related to financial calculations.
### Spreadsheet Details:
1. **Formula Bar:**
- The formula displayed here is:
```
=NPER(0.075,0,-21600,330000)
```
- `NPER` function in Excel is used to calculate the number of periods for an investment based on periodic, constant payments and a constant interest rate.
- Here, `0.075` is the interest rate, `0` is the payment amount per period, `-21600` is the present value, and `330000` is the future value.
2. **Data in Cells:**
- **Cell A1:** 10%
- **Cell A2:** 12%
- **Cell A3:** =NPER(0.075,0,-21600,330000)
- **Cell A4:** 37.69876105 (This appears to be the calculated result of the `NPER` formula)
- **Cell A5:** ($42,888.08) (This appears to be a negative dollar amount, potentially the result of another formula or calculation outside the currently visible cells)
### Explanation of the NPER Function:
The `NPER` function syntax is:
```
=NPER(rate, pmt, pv, [fv], [type])
```
- `rate`: Interest rate per period.
- `pmt`: Payment made each period; it cannot change over the life of the investment. Typically, `pmt` includes principal and interest but no other fees or taxes.
- `pv`: Present value, or the total amount that a series of future payments is worth now.
- `fv`: Future value, or a cash balance you want to attain after the last payment is made. If `fv` is omitted, it is assumed to be 0.
- `type`: Optional; type is the timing of the payment. 0 indicates the end of the period, and 1 indicates the beginning of the period.
### Summary:
This example demonstrates the usage of the `NPER` function to calculate the number of periods required for an investment to grow to a specific future value. The data shows realistic percentage rates and a practical calculation outcome as seen in cell A4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff6323c-cf7e-493a-b269-a8fbd92b416a%2F151016da-c7a0-4695-b08a-3f9b0bbdeaa0%2F98w3i0n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Excel Formula and Data Example
### Description:
The image shows a spreadsheet in Microsoft Excel containing a formula and some numerical data. This is an educational example related to financial calculations.
### Spreadsheet Details:
1. **Formula Bar:**
- The formula displayed here is:
```
=NPER(0.075,0,-21600,330000)
```
- `NPER` function in Excel is used to calculate the number of periods for an investment based on periodic, constant payments and a constant interest rate.
- Here, `0.075` is the interest rate, `0` is the payment amount per period, `-21600` is the present value, and `330000` is the future value.
2. **Data in Cells:**
- **Cell A1:** 10%
- **Cell A2:** 12%
- **Cell A3:** =NPER(0.075,0,-21600,330000)
- **Cell A4:** 37.69876105 (This appears to be the calculated result of the `NPER` formula)
- **Cell A5:** ($42,888.08) (This appears to be a negative dollar amount, potentially the result of another formula or calculation outside the currently visible cells)
### Explanation of the NPER Function:
The `NPER` function syntax is:
```
=NPER(rate, pmt, pv, [fv], [type])
```
- `rate`: Interest rate per period.
- `pmt`: Payment made each period; it cannot change over the life of the investment. Typically, `pmt` includes principal and interest but no other fees or taxes.
- `pv`: Present value, or the total amount that a series of future payments is worth now.
- `fv`: Future value, or a cash balance you want to attain after the last payment is made. If `fv` is omitted, it is assumed to be 0.
- `type`: Optional; type is the timing of the payment. 0 indicates the end of the period, and 1 indicates the beginning of the period.
### Summary:
This example demonstrates the usage of the `NPER` function to calculate the number of periods required for an investment to grow to a specific future value. The data shows realistic percentage rates and a practical calculation outcome as seen in cell A4
![### Related to Checkpoint 5.5 (Solving for n)
**Scenario:**
Jack asked Jill to marry him, and she has accepted under one condition: Jack must buy her a new $330,000 Rolls-Royce Phantom. Jack currently has $21,600 that he may invest. He has found a mutual fund with an expected annual return of 7.5 percent in which he will place the money. How long will it take Jack to win Jill's hand in marriage? Ignore taxes and inflation.
---
**Activity:**
The number of years it will take for Jack to win Jill’s hand in marriage is \_\_\_\_ years. (Round to one decimal place.)
---
**Instructions:**
1. Determine how long it will take for Jack's investment to grow to $330,000.
2. Use the formula for compound interest to solve for the number of years (n).
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in percent).
- \( n \) is the number of years the money is invested.
Given:
- \( A = 330,000 \)
- \( P = 21,600 \)
- \( r = 7.5\% \)
Solve for \( n \):
\[ 330,000 = 21,600 \left(1 + \frac{7.5}{100}\right)^n \]
\[ 330,000 = 21,600 \left(1.075\right)^n \]
Take the natural logarithm (ln) of both sides to solve for \( n \):
\[ \ln(330,000) = \ln\left[21,600 \left(1.075^n\right)\right] \]
\[ \ln(330,000) = \ln(21,600) + \ln\left(1.075^n\right) \]
\[ \ln(330,000) - \ln(21,600) = n \cdot \ln(1.075) \]
\[ n = \frac{\ln(330,000) - \ln(21,600)}{\ln(1.075](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff6323c-cf7e-493a-b269-a8fbd92b416a%2F151016da-c7a0-4695-b08a-3f9b0bbdeaa0%2F0mb4kep_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Related to Checkpoint 5.5 (Solving for n)
**Scenario:**
Jack asked Jill to marry him, and she has accepted under one condition: Jack must buy her a new $330,000 Rolls-Royce Phantom. Jack currently has $21,600 that he may invest. He has found a mutual fund with an expected annual return of 7.5 percent in which he will place the money. How long will it take Jack to win Jill's hand in marriage? Ignore taxes and inflation.
---
**Activity:**
The number of years it will take for Jack to win Jill’s hand in marriage is \_\_\_\_ years. (Round to one decimal place.)
---
**Instructions:**
1. Determine how long it will take for Jack's investment to grow to $330,000.
2. Use the formula for compound interest to solve for the number of years (n).
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in percent).
- \( n \) is the number of years the money is invested.
Given:
- \( A = 330,000 \)
- \( P = 21,600 \)
- \( r = 7.5\% \)
Solve for \( n \):
\[ 330,000 = 21,600 \left(1 + \frac{7.5}{100}\right)^n \]
\[ 330,000 = 21,600 \left(1.075\right)^n \]
Take the natural logarithm (ln) of both sides to solve for \( n \):
\[ \ln(330,000) = \ln\left[21,600 \left(1.075^n\right)\right] \]
\[ \ln(330,000) = \ln(21,600) + \ln\left(1.075^n\right) \]
\[ \ln(330,000) - \ln(21,600) = n \cdot \ln(1.075) \]
\[ n = \frac{\ln(330,000) - \ln(21,600)}{\ln(1.075
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