these payments are shown below. Also shown are the monthly interest rates that apply to each interval of time. What the P-equivalent of Will's payments on January 15? Q Jan. 15 April 15 June 15 Sept. 15 i=1/4% i=1/2% i=3/4% mo. I mo. mo. $10,000 $12,000 $13,000 $10,000 The P-equivalent of Will's payments on January 15 is $ *** (Round to the nearest dollar.)
these payments are shown below. Also shown are the monthly interest rates that apply to each interval of time. What the P-equivalent of Will's payments on January 15? Q Jan. 15 April 15 June 15 Sept. 15 i=1/4% i=1/2% i=3/4% mo. I mo. mo. $10,000 $12,000 $13,000 $10,000 The P-equivalent of Will's payments on January 15 is $ *** (Round to the nearest dollar.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![On this educational website, we explore the concept of present value in the context of quarterly estimated income tax payments.
### Problem Statement:
Will is required to make quarterly estimated income tax payments to the Internal Revenue Service. The amounts and timing of these payments are as follows:
- **January 15**: $10,000
- **April 15**: $12,000
- **June 15**: $13,000
- **September 15**: $10,000
Along with payment dates, the monthly interest rates applicable to each interval are also provided:
- From January 15 to April 15, the monthly interest rate is \( i = \frac{1}{4}\% \).
- From April 15 to June 15, the monthly interest rate is \( i = \frac{1}{2}\% \).
- From June 15 to September 15, the monthly interest rate is \( i = \frac{3}{4}\% \).
### Objective:
Calculate the Present Value (P-equivalent) of Will's payments on January 15.
### Graphical Explanation:
The timeline showcases four payment dates indicated with arrows pointing downwards along with the corresponding amounts and monthly interest rates — cumulatively providing a clear visual understanding of the financial scenario across the timeline.
### Calculation:
To determine the P-equivalent, each payment must be discounted back to the present value at January 15 using the specified interest rates for each period. The formula used to calculate the present value for each payment is:
\[ PV = \frac{FV}{(1 + i)^n} \]
where \( PV \) is the present value, \( FV \) is the future value or payment amount, \( i \) is the interest rate for the period, and \( n \) is the number of periods.
### Conclusion:
Perform the calculation for each payment and sum these present values to find the total P-equivalent as of January 15. The final answer should be rounded to the nearest dollar.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57ce95b0-55bf-4b74-8a30-95af5babada9%2F5d5dd759-0cae-4061-b283-7877f03d08ab%2F8rb30x9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:On this educational website, we explore the concept of present value in the context of quarterly estimated income tax payments.
### Problem Statement:
Will is required to make quarterly estimated income tax payments to the Internal Revenue Service. The amounts and timing of these payments are as follows:
- **January 15**: $10,000
- **April 15**: $12,000
- **June 15**: $13,000
- **September 15**: $10,000
Along with payment dates, the monthly interest rates applicable to each interval are also provided:
- From January 15 to April 15, the monthly interest rate is \( i = \frac{1}{4}\% \).
- From April 15 to June 15, the monthly interest rate is \( i = \frac{1}{2}\% \).
- From June 15 to September 15, the monthly interest rate is \( i = \frac{3}{4}\% \).
### Objective:
Calculate the Present Value (P-equivalent) of Will's payments on January 15.
### Graphical Explanation:
The timeline showcases four payment dates indicated with arrows pointing downwards along with the corresponding amounts and monthly interest rates — cumulatively providing a clear visual understanding of the financial scenario across the timeline.
### Calculation:
To determine the P-equivalent, each payment must be discounted back to the present value at January 15 using the specified interest rates for each period. The formula used to calculate the present value for each payment is:
\[ PV = \frac{FV}{(1 + i)^n} \]
where \( PV \) is the present value, \( FV \) is the future value or payment amount, \( i \) is the interest rate for the period, and \( n \) is the number of periods.
### Conclusion:
Perform the calculation for each payment and sum these present values to find the total P-equivalent as of January 15. The final answer should be rounded to the nearest dollar.
Expert Solution
Step 1: Define cash flow statement:-
A cash flow statement is a financial statement that displays the inflow and outflow of cash for a business over the course of a given accounting period. Accounting professionals utilise these statements to record, track, and report cash inflows and outflows for their clients' businesses.
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