You just inherited some money, and you decide to put $70,000 in an account that pays 3.25% interest, which you will use to establish an annuity that will pay for your vacations for the next ten years. How much can you withdraw from the account in each of the ten years? $8,044.56 $7,826.10 $6,241.51 $8,311.18
You just inherited some money, and you decide to put $70,000 in an account that pays 3.25% interest, which you will use to establish an annuity that will pay for your vacations for the next ten years. How much can you withdraw from the account in each of the ten years? $8,044.56 $7,826.10 $6,241.51 $8,311.18
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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![### Annuity Withdrawal Calculation
#### Scenario:
You have inherited $70,000, which you decide to invest in an account with an annual interest rate of 3.25%. This investment will be used to establish an annuity for funding vacations over the next ten years. The question is: **How much can you withdraw from this account each year for the next ten years?**
#### Options:
- $8,044.56
- $7,826.10
- $6,241.51
- $8,311.18
To solve this problem, you'll need to use the formula for calculating annuity withdrawals:
\[ P = \frac{r \times PV}{1 - (1 + r)^{-n}} \]
Where:
- \( P \) is the annual payment
- \( r \) is the annual interest rate (in decimal form)
- \( PV \) is the present value (initial investment)
- \( n \) is the number of years
Plug in the values:
- \( PV = \$70,000 \)
- \( r = 0.0325 \)
- \( n = 10 \)
#### Calculation Steps:
1. **Convert Interest Rate to Decimal**: \( 3.25\% = 0.0325 \)
2. **Substitute Values into Formula**:
\[
P = \frac{0.0325 \times 70000}{1 - (1 + 0.0325)^{-10}}
\]
3. **Calculate**: This gives the amount you can withdraw each year.
Using these calculations helps in selecting the correct option and effectively managing financial planning for anticipated annual withdrawals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc790c56e-6040-4fac-977f-3f8f6b1c52b4%2Fa787f49f-6734-46ae-af65-13ec5042bc2a%2Fjgx0xke_processed.png&w=3840&q=75)
Transcribed Image Text:### Annuity Withdrawal Calculation
#### Scenario:
You have inherited $70,000, which you decide to invest in an account with an annual interest rate of 3.25%. This investment will be used to establish an annuity for funding vacations over the next ten years. The question is: **How much can you withdraw from this account each year for the next ten years?**
#### Options:
- $8,044.56
- $7,826.10
- $6,241.51
- $8,311.18
To solve this problem, you'll need to use the formula for calculating annuity withdrawals:
\[ P = \frac{r \times PV}{1 - (1 + r)^{-n}} \]
Where:
- \( P \) is the annual payment
- \( r \) is the annual interest rate (in decimal form)
- \( PV \) is the present value (initial investment)
- \( n \) is the number of years
Plug in the values:
- \( PV = \$70,000 \)
- \( r = 0.0325 \)
- \( n = 10 \)
#### Calculation Steps:
1. **Convert Interest Rate to Decimal**: \( 3.25\% = 0.0325 \)
2. **Substitute Values into Formula**:
\[
P = \frac{0.0325 \times 70000}{1 - (1 + 0.0325)^{-10}}
\]
3. **Calculate**: This gives the amount you can withdraw each year.
Using these calculations helps in selecting the correct option and effectively managing financial planning for anticipated annual withdrawals.
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