What payments must be made at the end of each quarter to an RRSP earning 7.5% compounded annually so that its value 812 years from now will be $15,000? (Do not round intermediate calculations and round your final answer to 2 decimal places.) PMT $
What payments must be made at the end of each quarter to an RRSP earning 7.5% compounded annually so that its value 812 years from now will be $15,000? (Do not round intermediate calculations and round your final answer to 2 decimal places.) PMT $
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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![### Financial Calculation Scenario:
**Problem Statement:**
What payments must be made at the end of each quarter to an RRSP earning 7.5% compounded annually so that its value 81.2 years from now will be $15,000? (Do not round intermediate calculations and round your final answer to 2 decimal places.) PMT $
**Explanation:**
To determine the quarterly payment (PMT) to an RRSP (Registered Retirement Savings Plan) earning an annual interest rate of 7.5%, compounded annually, with a target value of $15,000 in 81.2 years, we utilize the Future Value of an Annuity formula. The values given are:
- Interest rate (i): 7.5% per year
- Total time (t): 81.2 years
- Future Value (FV): $15,000
Since payments are made quarterly, we need to adjust the interest rate and the total number of periods to reflect quarterly payments:
- Quarterly interest rate (i_q): 7.5% / 4 = 1.875% per quarter
- Total number of quarters (n): 81.2 years * 4 = 324.8 quarters
Using the formula for the Future Value of an Ordinary Annuity:
\[ FV = PMT \times \left(\frac{(1 + i)^n - 1}{i}\right) \]
Where FV is the future value, PMT is the payment per period, i is the quarterly interest rate, and n is the number of periods.
When solved for PMT, the formula becomes:
\[ PMT = \frac{FV \times i}{(1 + i)^n -1 } \]
Substituting the known values:
\[ PMT = \frac{15000 \times 0.01875}{(1 + 0.01875)^{324.8} -1 } \]
Perform the intermediate calculations accurately and ensure the final answer is presented rounded to two decimal places.
**Note:** Ensure to use precise values during intermediate calculations to prevent rounding errors influencing the final result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F136a9916-8a5d-490b-a1c4-57e644d5608a%2F9d2e6d8b-e263-4531-8d7e-d9fabb13c172%2Fyba3512_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Financial Calculation Scenario:
**Problem Statement:**
What payments must be made at the end of each quarter to an RRSP earning 7.5% compounded annually so that its value 81.2 years from now will be $15,000? (Do not round intermediate calculations and round your final answer to 2 decimal places.) PMT $
**Explanation:**
To determine the quarterly payment (PMT) to an RRSP (Registered Retirement Savings Plan) earning an annual interest rate of 7.5%, compounded annually, with a target value of $15,000 in 81.2 years, we utilize the Future Value of an Annuity formula. The values given are:
- Interest rate (i): 7.5% per year
- Total time (t): 81.2 years
- Future Value (FV): $15,000
Since payments are made quarterly, we need to adjust the interest rate and the total number of periods to reflect quarterly payments:
- Quarterly interest rate (i_q): 7.5% / 4 = 1.875% per quarter
- Total number of quarters (n): 81.2 years * 4 = 324.8 quarters
Using the formula for the Future Value of an Ordinary Annuity:
\[ FV = PMT \times \left(\frac{(1 + i)^n - 1}{i}\right) \]
Where FV is the future value, PMT is the payment per period, i is the quarterly interest rate, and n is the number of periods.
When solved for PMT, the formula becomes:
\[ PMT = \frac{FV \times i}{(1 + i)^n -1 } \]
Substituting the known values:
\[ PMT = \frac{15000 \times 0.01875}{(1 + 0.01875)^{324.8} -1 } \]
Perform the intermediate calculations accurately and ensure the final answer is presented rounded to two decimal places.
**Note:** Ensure to use precise values during intermediate calculations to prevent rounding errors influencing the final result.
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