What do i enter for N, i,y, PMT, PV and FV on a finance calculator to solve the problem below.

Question

Derek currently has $13,466.00 in an account that pays 4.00%. He will withdraw $5,517.00 every other year beginning next year until he has taken 8.00 withdrawals. He will deposit $13466.0 every other year beginning two years from today until he has made 8.0 deposits. How much will be in the account 24.00 years from today?

Answer 1

To solve this problem, you need to break it down into two separate cases: the withdrawals and the deposits.

Step 1: Understanding the Problem

1. Withdrawals:

   • Amount: $5,517
   • Frequency: Every other year (starting from year 1)
   • Total Time Frame: 16 years of withdrawals (since he withdraws 8 times)
   • Interest Rate: 4% per year

2. Deposits:

   • Amount: $13,466
   • Frequency: Every other year (starting from year 2)
   • Total Time Frame: 16 years of deposits (since he deposits 8 times)
   • Interest Rate: 4% per year

Step 2: Set Up Withdrawals for a Finance Calculator

For Withdrawals:

1. N (number of periods): 16 (since he withdraws 8 times over 16 years)
2. i (interest rate per period): 4% (annual interest rate)
3. PMT (payment per period): -5,517 (withdrawals are negative cash flows)
4. PV (present value): You will need to enter the current value of the account which is $13,466 when calculating future value after withdrawals.
5. FV: This will be what we are solving for, after all withdrawals.

Calculation:

• After calculating the future value after all withdrawals using the finance calculator, note the resultant value (let's call it FV_withdrawals).

Step 3: Set Up Deposits for the Calculator

For Deposits:

1. N (number of periods): 16 (since he deposits 8 times over 16 years)
2. i (interest rate per period): 4% (annual interest rate)
3. PMT (payment per period): 13,466 (deposits are positive cash flows)
4. PV (present value): 0 (assuming we're calculating from the future value of deposits)
5. FV: This will also be calculated.

Calculation:

• After calculating the future value of deposits using the finance calculator, note the resultant value (let's call it FV_deposits).

Step 4: Combine Results

• The final account balance after 24 years will be the future value of the initial amount after accounting for withdrawals plus the future value of the deposits.

Formula Recap

• \(FV = FV_{\text{initial}} - FV_{\text{withdrawals}} + FV_{\text{deposits}}\)

Notes

• Ensure that your calculator is set to the correct compounding option (e.g. every period).
• Always double-check configurations since some calculators might have different notations or methods for entering values.
• The total duration is less than 24 years; you're considering intervals based on every other year, not simply counting years, so make sure to reflect that in \(N\).

This setup will help you accurately assess the scenario with clear organization and breakdowns of each component involved.

Answer 2

I got FV_withdrawal=10,806.57327 and FV_deposit=-69,408. What do I do next to solve?

Answer 3

It looks like you've calculated two separate future values based on the withdrawals and deposits. However, it seems there might have been an issue with the sign (or calculation) of your future value for the deposits, as it should typically result in a positive future value if you're making positive deposits.

Let’s clarify the two future values you've got and then compute the final amount in the account after 24 years:

Step 1: Review Your Future Values

1. Future Value from Withdrawals (FV_withdrawal):

   • You calculated this to be $10,806.57 (this is what remains in the account after withdrawals).
   • Note: If future value calculations (such as the ending balance) give negative values for withdrawals, make sure you’re using the correct PMT (withdrawals should typically be a negative cash flow in this context).

2. Future Value from Deposits:

   • You calculated this to be -$69,408 (this seems incorrect, as deposits should compound positively). Please recheck the calculation here. The deposits should yield a positive future value.

Step 2: Recalculate Future Value of Deposits

If your calculated future value for the deposits was indeed negative:

1. Check the input for the deposits:
   • N: Should be 16 (since 8 deposits are made every other year over 16 years).
   • i: Should be 4% (0.04).
   • PMT: Should be 13,466 (as a positive value).
   • PV: Should be 0 since you start from the future value of the existing account balance.

Thus, your equation should look something like: \[ FV_{\text{deposits}} = PMT \times \left( \frac{(1 + r)^n - 1}{r} \right) \] where \( PMT = 13,466 \), \( r = 0.04 \), and \( n = 8 \) (the number of deposits).

Example Calculation for FV_deposits:

To compute the future value for deposits:

\[ FV_{\text{deposits}} = 13,466 \times \left( \frac{(1 + 0.04)^8 - 1}{0.04} \right) \]

Calculate this value first.

Step 3: Combine the Future Values

Once you have the correct positive value for FV_deposits:

1. Add FV_withdrawal to the corrected FV_deposits:

\[ \text{Total Future Value} = FV_{\text{deposits}} + FV_{\text{withdrawal}} \]

Example:

• If we assume you recalculate and find FV_deposits = X (ensure it's positive), then: \[ \text{Total Future Value} = FV_{\text{withdrawal}} + FV_{\text{deposits}} = 10,806.57 + X \]

Final Note

Once you compute these values correctly, adding them will give you the total amount in Derek's account after 24 years. Please report back with any new figures if you need further assistance or validation on them!