Find the periodic payments PMT necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $50,000 in a fund paying 5% per year, with monthly payments for 5 years, if the fund contains $10,000 at the start PMT = $ %3D
Find the periodic payments PMT necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $50,000 in a fund paying 5% per year, with monthly payments for 5 years, if the fund contains $10,000 at the start PMT = $ %3D
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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Question
![**Title: Calculating Periodic Payments for Annuity Accumulation**
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**Objective:**
Find the periodic payments \( PMT \) necessary to accumulate the given amount in an annuity account. The scenario assumes end-of-period deposits and compounding at the same intervals as deposits. Answers should be rounded to the nearest cent.
---
**Problem Statement:**
You need to determine the periodic payments required to accumulate $50,000 in a fund. The fund offers a 5% annual interest rate, with monthly payments for 5 years. Initially, the fund contains $10,000.
**Formula:**
\[ PMT = ? \]
**Parameters:**
- **Future Value (FV):** $50,000
- **Initial Principal (PV):** $10,000
- **Interest Rate:** 5% per year
- **Compounding:** Monthly
- **Time Period:** 5 years
---
**Explanation:**
To solve for \( PMT \), apply the future value of an annuity formula. This involves determining the regular payment amount needed to meet the $50,000 goal, considering the existing $10,000 and compounded interest.
**Note:** This exercise requires understanding of annuity formulas and interest compounding principles. Calculators or financial software might be needed for accurate computation.
---
**Visual Aids:**
Since this task does not include graphs or diagrams, consider using tables or charts to illustrate hypothetical scenarios or the effect of varying interest rates and time periods on annuity growth.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F567b405c-a8ec-4133-a9f4-1b3e3fcbb4f8%2F2ebb3fdc-0406-4f72-aa9e-7ee606f62869%2Fzsatgf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Periodic Payments for Annuity Accumulation**
---
**Objective:**
Find the periodic payments \( PMT \) necessary to accumulate the given amount in an annuity account. The scenario assumes end-of-period deposits and compounding at the same intervals as deposits. Answers should be rounded to the nearest cent.
---
**Problem Statement:**
You need to determine the periodic payments required to accumulate $50,000 in a fund. The fund offers a 5% annual interest rate, with monthly payments for 5 years. Initially, the fund contains $10,000.
**Formula:**
\[ PMT = ? \]
**Parameters:**
- **Future Value (FV):** $50,000
- **Initial Principal (PV):** $10,000
- **Interest Rate:** 5% per year
- **Compounding:** Monthly
- **Time Period:** 5 years
---
**Explanation:**
To solve for \( PMT \), apply the future value of an annuity formula. This involves determining the regular payment amount needed to meet the $50,000 goal, considering the existing $10,000 and compounded interest.
**Note:** This exercise requires understanding of annuity formulas and interest compounding principles. Calculators or financial software might be needed for accurate computation.
---
**Visual Aids:**
Since this task does not include graphs or diagrams, consider using tables or charts to illustrate hypothetical scenarios or the effect of varying interest rates and time periods on annuity growth.
---
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