You wish to have a pension of $100,000 a year for 25 years. How much money must you have saved if you can earn 8% interest compounded annually to make your wish a reality. The first payment occurs one year from now? O a Ob $1,128,433.33 $1,067,477.62 Oc $1,487,320.09 Od $1,250,000.00
You wish to have a pension of $100,000 a year for 25 years. How much money must you have saved if you can earn 8% interest compounded annually to make your wish a reality. The first payment occurs one year from now? O a Ob $1,128,433.33 $1,067,477.62 Oc $1,487,320.09 Od $1,250,000.00
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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![**Effective Financial Planning: Calculating Required Savings for a Pension**
**Question:**
You wish to have a pension of $100,000 a year for 25 years. How much money must you have saved if you can earn 8% interest compounded annually to make your wish a reality? The first payment occurs one year from now.
**Options:**
- a. $1,128,433.33
- b. $1,067,477.62
- c. $1,487,320.09
- d. $1,250,000.00
**Explanation:**
To determine how much money you need to save to receive $100,000 annually for 25 years with an 8% annual interest rate, we use the present value of an annuity formula. This calculation takes into account the future payments and discounts them back to their present value, considering the compound interest rate.
When calculating the present value (PV) of an annuity, the formula is:
\[ PV = P \times \left(1 - \left(1 + r\right)^{-n}\right) / r \]
Where:
- \(P\) is the annual payment ($100,000).
- \(r\) is the annual interest rate (0.08).
- \(n\) is the number of years (25).
Inserting the values, you can determine the correct amount needed.
Choose the correct option from above based on your evaluation and ensure your financial plan meets your future needs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78db42f9-6d62-48c9-a117-b436e469106b%2F65f63d20-4d5b-44a9-9bb6-849440784f3c%2F9wew33n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Effective Financial Planning: Calculating Required Savings for a Pension**
**Question:**
You wish to have a pension of $100,000 a year for 25 years. How much money must you have saved if you can earn 8% interest compounded annually to make your wish a reality? The first payment occurs one year from now.
**Options:**
- a. $1,128,433.33
- b. $1,067,477.62
- c. $1,487,320.09
- d. $1,250,000.00
**Explanation:**
To determine how much money you need to save to receive $100,000 annually for 25 years with an 8% annual interest rate, we use the present value of an annuity formula. This calculation takes into account the future payments and discounts them back to their present value, considering the compound interest rate.
When calculating the present value (PV) of an annuity, the formula is:
\[ PV = P \times \left(1 - \left(1 + r\right)^{-n}\right) / r \]
Where:
- \(P\) is the annual payment ($100,000).
- \(r\) is the annual interest rate (0.08).
- \(n\) is the number of years (25).
Inserting the values, you can determine the correct amount needed.
Choose the correct option from above based on your evaluation and ensure your financial plan meets your future needs.
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