Question
Tabitha saved 400,000
for retirement. She wants to withdraw part of that money from her retirement account each month and wants it to last 20 years. Her account has a
interest rate. Use the payout annuity formula to calculate how much she will be able to withdraw each month for those 20 years. When solving, round numbers to the nearest hundred-thousandth. Round your final answer to the nearest cent.
1,666.67
1,766.67
2,368.00
2,865.74
for retirement. She wants to withdraw part of that money from her retirement account each month and wants it to last 20 years. Her account has a
interest rate. Use the payout annuity formula to calculate how much she will be able to withdraw each month for those 20 years. When solving, round numbers to the nearest hundred-thousandth. Round your final answer to the nearest cent.
1,666.67
1,766.67
2,368.00
2,865.74
Answers
GPT-4o mini
To determine how much Tabitha can withdraw each month from her retirement account, we can use the formula for an annuity, which is given by:
\[
P = \frac{rPV}{1 - (1 + r)^{-n}}
\]
Where:
- \( P \) is the monthly withdrawal amount.
- \( PV \) is the present value of the annuity (amount saved, which is $400,000 in this case).
- \( r \) is the monthly interest rate (annual interest rate divided by 12).
- \( n \) is the total number of withdrawals (months of withdrawals, which is 20 years x 12 months/year).
Assuming the interest rate is not provided, we cannot calculate a specific amount unless given. However, I will illustrate how to compute for an interest rate example.
If, for example, we assume an annual interest rate of **5%**, we would have:
- Convert it to monthly:
\[
r = \frac{5\%}{12} = 0.00416667
\]
- Determine total number of months:
\[
n = 20 \times 12 = 240
\]
Now plug these values into the annuity formula:
\[
P = \frac{0.00416667 \times 400,000}{1 - (1 + 0.00416667)^{-240}}
\]
Calculating \( (1 + r)^{-n} \):
\[
(1 + 0.00416667)^{-240} \approx (1.00416667)^{-240} \approx 0.364139
\]
Now substituting back into the formula:
\[
P = \frac{0.00416667 \times 400,000}{1 - 0.364139} = \frac{1666.67}{0.635861} \approx 2611.34
\]
Thus, with a **5% interest rate**, the monthly withdrawal would be approximately **$2,611.34**.
If you know the specific interest rate, please provide it, and I can give you the exact calculation corresponding to that rate.
The final answer from the given options would depend on the correct interest rate assumption.
\[
P = \frac{rPV}{1 - (1 + r)^{-n}}
\]
Where:
- \( P \) is the monthly withdrawal amount.
- \( PV \) is the present value of the annuity (amount saved, which is $400,000 in this case).
- \( r \) is the monthly interest rate (annual interest rate divided by 12).
- \( n \) is the total number of withdrawals (months of withdrawals, which is 20 years x 12 months/year).
Assuming the interest rate is not provided, we cannot calculate a specific amount unless given. However, I will illustrate how to compute for an interest rate example.
If, for example, we assume an annual interest rate of **5%**, we would have:
- Convert it to monthly:
\[
r = \frac{5\%}{12} = 0.00416667
\]
- Determine total number of months:
\[
n = 20 \times 12 = 240
\]
Now plug these values into the annuity formula:
\[
P = \frac{0.00416667 \times 400,000}{1 - (1 + 0.00416667)^{-240}}
\]
Calculating \( (1 + r)^{-n} \):
\[
(1 + 0.00416667)^{-240} \approx (1.00416667)^{-240} \approx 0.364139
\]
Now substituting back into the formula:
\[
P = \frac{0.00416667 \times 400,000}{1 - 0.364139} = \frac{1666.67}{0.635861} \approx 2611.34
\]
Thus, with a **5% interest rate**, the monthly withdrawal would be approximately **$2,611.34**.
If you know the specific interest rate, please provide it, and I can give you the exact calculation corresponding to that rate.
The final answer from the given options would depend on the correct interest rate assumption.