With a present value of $125,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7.8%, compounded quarterly? (Round your answer to the nearest cent.)
With a present value of $125,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7.8%, compounded quarterly? (Round your answer to the nearest cent.)
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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![**Problem Statement:**
With a present value of $125,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7.8%, compounded quarterly? (Round your answer to the nearest cent.)
**Incorrect Attempt:**
$4,608.61 ✘
**Explanation:**
This question involves calculating the periodic withdrawal that can be made from a sum of money, given a specific interest rate and compounding frequency. The present value is $125,000 and the interest rate is 7.8%, compounded quarterly. The time frame is 10 years.
To find the correct withdrawal amount, use the formula for the Present Value of an Annuity:
\[ PV = PMT \times \left(\frac{1 - (1 + r)^{-nt}}{r}\right) \]
Where:
- \( PV \) is the present value ($125,000)
- \( PMT \) is the payment (withdrawal amount per period)
- \( r \) is the quarterly interest rate (\(\frac{7.8\%}{4} = 1.95\%\))
- \( n \) is the number of compounding periods per year (4 for quarterly)
- \( t \) is the total number of years (10)
Plug the known values into the formula to solve for \( PMT \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feafecdb5-6a00-4b1b-9bab-c3b276507665%2F7d43b1fb-e39f-41cf-bd7e-6ec0c4c4ce5c%2Fy4plhgo_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
With a present value of $125,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7.8%, compounded quarterly? (Round your answer to the nearest cent.)
**Incorrect Attempt:**
$4,608.61 ✘
**Explanation:**
This question involves calculating the periodic withdrawal that can be made from a sum of money, given a specific interest rate and compounding frequency. The present value is $125,000 and the interest rate is 7.8%, compounded quarterly. The time frame is 10 years.
To find the correct withdrawal amount, use the formula for the Present Value of an Annuity:
\[ PV = PMT \times \left(\frac{1 - (1 + r)^{-nt}}{r}\right) \]
Where:
- \( PV \) is the present value ($125,000)
- \( PMT \) is the payment (withdrawal amount per period)
- \( r \) is the quarterly interest rate (\(\frac{7.8\%}{4} = 1.95\%\))
- \( n \) is the number of compounding periods per year (4 for quarterly)
- \( t \) is the total number of years (10)
Plug the known values into the formula to solve for \( PMT \).
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