You want to be able to withdraw $25,000 from your account each year for 20 years after you retire. If you expect to retire in 25 years and your account earns 7% interest while saving for retirement and 6.7% interest while retired

Round your answers to the nearest cents as needed.
a) How much will you need to have when you retire?
b) How much will you need to deposit each month until retirement to achieve your retirement goals?
c) How much did you deposit into you retirement account?
d) How much did you receive in payments during retirement?
e) How much of the money you received was interest?

I need to know exactly your getting these answers, I only have one shot at this. I have tried everything I was taught and I'm not understanding where to start. Please and thank you!

To calculate the answers, we will use the following steps:

Step 1: Calculate the future value (FV) of the annual withdrawals during retirement.
Step 2: Calculate the present value (PV) needed for retirement.
Step 3: Determine the monthly deposit required to achieve the retirement goal.
Step 4: Calculate the total amount deposited into the retirement account.
Step 5: Calculate the total amount received in payments during retirement.
Step 6: Calculate the amount of the received money that was interest.

Let's begin with the calculations:

Step 1: Calculate the future value of the annual withdrawals during retirement.

Using the future value of an annuity formula:

FV = P * [((1 + r)^n) - 1] / r

Where:
FV = future value (the total amount you want to withdraw during retirement)
P = annual withdrawal amount ($25,000)
r = interest rate during retirement (6.7%)
n = number of years in retirement (20)

FV = $25,000 * [((1 + 0.067)^20) - 1] / 0.067
FV ≈ $392,182.97

Therefore, you will need approximately $392,182.97 when you retire.

Step 2: Calculate the present value needed for retirement.

The present value (PV) represents the amount you need to have saved by the time you retire to achieve the desired future value. Since the interest rate is the same during retirement as it is while saving for retirement, we can use the present value of an ordinary annuity formula:

PV = FV / (1 + r)^n

Where:
PV = present value (the amount you need to have when you retire)
FV = future value ($392,182.97)
r = interest rate (7%)
n = number of years until retirement (25)

PV = $392,182.97 / (1 + 0.07)^25
PV ≈ $53,225.45

Therefore, you will need approximately $53,225.45 saved by the time you retire.

Step 3: Determine the monthly deposit required to achieve the retirement goal.

To calculate the monthly deposit needed until retirement, we can use the present value of an ordinary annuity formula:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Where:
PV = present value ($53,225.45)
PMT = monthly deposit
r = interest rate (7%)
n = number of months until retirement (25*12)

$53,225.45 = PMT * [(1 - (1 + 0.07)^(-25*12)) / 0.07]
PMT ≈ $98.91

Therefore, you will need to deposit approximately $98.91 each month until retirement to achieve your retirement goals.

Step 4: Calculate the total amount deposited into the retirement account.

The total amount deposited can be found by multiplying the monthly deposit by the number of months until retirement:

Total Deposits = PMT * n

Total Deposits = $98.91 * (25 * 12)
Total Deposits ≈ $29,673.60

Therefore, you will deposit approximately $29,673.60 into your retirement account.

Step 5: Calculate the total amount received in payments during retirement.

The total amount received can be found by multiplying the annual withdrawal amount by the number of years in retirement:

Total Payments = P * n

Total Payments = $25,000 * 20
Total Payments = $500,000

Therefore, you will receive a total of $500,000 in payments during retirement.

Step 6: Calculate the amount of the received money that was interest.

The interest can be calculated by subtracting the total amount deposited from the total payments received:

Interest = Total Payments - Total Deposits

Interest = $500,000 - $29,673.60
Interest ≈ $470,326.40

Therefore, approximately $470,326.40 of the money you received during retirement will be interest.

By following these steps, you should be able to calculate the exact answers for all the questions.

To answer these questions, we can use the concept of the future value of an annuity. The future value of an annuity calculates how much money you will have in the future by making regular deposits or withdrawals at a certain interest rate over a set period of time.

Let's go through each question step by step:

a) How much will you need to have when you retire?
To determine how much you will need when you retire, we need to calculate the future value of $25,000 withdrawals per year for 20 years at an interest rate of 6.7%. We can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:
FV = Future Value
P = Annuity Payment (withdrawal)
r = Interest Rate per period
n = Number of periods

In this case, P = $25,000, r = 6.7% (or 0.067), and n = 20. Plugging these values into the formula:

FV = $25,000 * [(1 + 0.067)^20 - 1] / 0.067

Using a financial calculator or spreadsheet, we find that the future value (the amount you will need when you retire) is approximately $337,160.73.

b) How much will you need to deposit each month until retirement to achieve your retirement goals?
To calculate the monthly deposit required, we use the formula for the present value of an ordinary annuity. The present value represents how much you need to deposit now in order to reach a specific future value.

PV = P * [(1 - (1 + r)^(-n))] / r

Where:
PV = Present Value
P = Annuity Payment (deposit)
r = Interest Rate per period
n = Number of periods

We can rearrange the formula to solve for P:

P = PV * r / [(1 - (1 + r)^(-n))]

In this case, PV (Present Value) is the future value we calculated in part a) ($337,160.73), r = 7% (or 0.07), and n = 25 (since you have 25 years until retirement). Plugging these values into the formula:

P = $337,160.73 * 0.07 / [(1 - (1 + 0.07)^(-25))]

By calculating this, we find that you need to deposit approximately $4,321.87 per month to achieve your retirement goals.

c) How much did you deposit into your retirement account?
To calculate the total amount deposited into the retirement account, multiply the monthly deposit by the number of months until retirement. In this case, you will be saving for 25 years or 300 months.

Total deposit = Monthly deposit * Number of months until retirement

Total deposit = $4,321.87 * 300 = $1,296,561.78

Therefore, you will have deposited approximately $1,296,561.78 into your retirement account.

d) How much did you receive in payments during retirement?
Since you are withdrawing $25,000 per year for 20 years during retirement, you can calculate the total payment received.

Total payment = Withdrawal per year * Number of years

Total payment = $25,000 * 20 = $500,000

You will receive a total payment of $500,000 during your retirement.

e) How much of the money you received was interest?
To calculate the interest earned, subtract the total deposit from the total payment received.

Interest earned = Total payment - Total deposit

Interest earned = $500,000 - $1,296,561.78

The interest earned on your retirement savings is approximately -$796,561.78 (negative because you withdrew more than you deposited).

Please note that these calculations are based on the formulas for annuity calculations and rounding errors may occur in the final answers. It's always a good idea to double-check the calculations and consult with a financial advisor for a more accurate analysis of your retirement plan.

543.98