Problem 5-7 Calculating Annuity Cash Flows [LO 1] For each of the following annuities, calculate the annuity payment. Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. Annuity Payment Future Value Years $ 24,350 $ 980,000 $ 796,000 133,000 SALA $ 8 38 24 15 Interest Rate 7% 9 10 6
Problem 5-7 Calculating Annuity Cash Flows [LO 1] For each of the following annuities, calculate the annuity payment. Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. Annuity Payment Future Value Years $ 24,350 $ 980,000 $ 796,000 133,000 SALA $ 8 38 24 15 Interest Rate 7% 9 10 6
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
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![# Problem 5-7: Calculating Annuity Cash Flows
## Objective:
Calculate the annuity payment for each of the following annuities.
### Instructions:
1. **Intermediate Calculations**: Do not round during intermediate calculations.
2. **Final Answers**: Round your answers to two decimal places, e.g., 32.16.
### Given Data:
Below is the table representing the Future Value, Years, and Interest Rate for various annuities. Your task is to calculate the corresponding Annuity Payment.
| Annuity Payment | Future Value | Years | Interest Rate |
|-----------------|--------------|-------|---------------|
| | $24,350 | 8 | 7% |
| | $980,000 | 38 | 9% |
| | $796,000 | 24 | 10% |
| | $133,000 | 15 | 6% |
### Steps to Calculate Annuity Payment:
1. **Identify the given values**: Future Value (FV), Number of Years (n), and Interest Rate (r).
2. **Use the Future Value of Annuity formula**:
\[ FV = P \times \frac{(1+r)^n - 1}{r} \]
Solving for the Annuity Payment (P):
\[ P = \frac{FV \times r}{(1+r)^n - 1} \]
### Calculations:
Calculate the annuity payment for each row in the provided data table using the formula above.
### Example:
For the first row:
- **Future Value (FV)**: $24,350
- **Years (n)**: 8
- **Interest Rate (r)**: 7% = 0.07
\[ P = \frac{24350 \times 0.07}{(1 + 0.07)^8 - 1} \]
Continue this process for all provided values to determine the annuity payments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4100da26-36bd-43a6-aafd-ee8e0ffe886a%2Fd3cfa149-eb3f-43e0-b9d6-f9946c86feb4%2Fdbgi5xd_processed.png&w=3840&q=75)
Transcribed Image Text:# Problem 5-7: Calculating Annuity Cash Flows
## Objective:
Calculate the annuity payment for each of the following annuities.
### Instructions:
1. **Intermediate Calculations**: Do not round during intermediate calculations.
2. **Final Answers**: Round your answers to two decimal places, e.g., 32.16.
### Given Data:
Below is the table representing the Future Value, Years, and Interest Rate for various annuities. Your task is to calculate the corresponding Annuity Payment.
| Annuity Payment | Future Value | Years | Interest Rate |
|-----------------|--------------|-------|---------------|
| | $24,350 | 8 | 7% |
| | $980,000 | 38 | 9% |
| | $796,000 | 24 | 10% |
| | $133,000 | 15 | 6% |
### Steps to Calculate Annuity Payment:
1. **Identify the given values**: Future Value (FV), Number of Years (n), and Interest Rate (r).
2. **Use the Future Value of Annuity formula**:
\[ FV = P \times \frac{(1+r)^n - 1}{r} \]
Solving for the Annuity Payment (P):
\[ P = \frac{FV \times r}{(1+r)^n - 1} \]
### Calculations:
Calculate the annuity payment for each row in the provided data table using the formula above.
### Example:
For the first row:
- **Future Value (FV)**: $24,350
- **Years (n)**: 8
- **Interest Rate (r)**: 7% = 0.07
\[ P = \frac{24350 \times 0.07}{(1 + 0.07)^8 - 1} \]
Continue this process for all provided values to determine the annuity payments.
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