Malika Agwani starts her career at the age of 25 and makes equal monthly deposits for 35 years into an annuity that earns 6.25% compounded monthly. She plans on retiring the age of 60 and would like to withdraw $3000 monthly for 25 years, bringing the account balance to $0. How much should Malika deposit monthly to accumulate enough to provide her with these $3000 monthly payments?

To calculate the amount Malika should deposit each month to accumulate enough for the $3000 monthly payments, we can use the concept of the future value of an annuity.

The future value of an annuity formula is:

FV = PMT x [(1 + r)^n - 1] / r

Where:
FV = Future Value (the amount Malika wishes to accumulate)
PMT = Monthly deposit amount
r = Monthly interest rate
n = Number of periods (in this case, the number of monthly deposits)

We are given the following information:
Starting age = 25
Retirement age = 60
Deposit period = 35 years (from age 25 to 60)
Withdrawal period = 25 years (from age 60 to 85)
Monthly interest rate = 6.25% compounded monthly
Monthly withdrawal amount = $3000

First, let's calculate the number of periods for the deposit period:
35 years x 12 months/year = 420 months

Next, let's calculate the number of periods for the withdrawal period:
25 years x 12 months/year = 300 months

Now, let's calculate the future value (FV) using the given withdrawal amount and periods:
FV = $3000 x [(1 + 0.0625/12)^300 - 1] / (0.0625/12)

Using a calculator or spreadsheet, the future value FV comes out to be approximately $1,651,334.89.

Now, let's rearrange the formula to solve for the monthly deposit amount (PMT):
PMT = FV x (r / [(1+r)^n - 1])

Substituting the values, we have:
PMT = $1,651,334.89 x (0.0625/12) / [(1 + 0.0625/12)^420 - 1]

Again, using a calculator or spreadsheet, the monthly deposit amount PMT comes out to be approximately $296.17.

Therefore, Malika should deposit approximately $296.17 each month to accumulate enough to provide her with $3000 monthly payments during retirement.

To calculate the monthly deposit required to accumulate enough to provide $3000 monthly payments for 25 years, we can use the formula for the present value of an annuity.

Step 1: Calculate the number of deposits
Since Malika starts her career at the age of 25 and plans on retiring at the age of 60, she will make deposits for a total of 60 - 25 = 35 years.

Step 2: Calculate the total number of periods
Since the deposits are made and the payments are withdrawn monthly, we need to calculate the total number of periods in months. Since there are 12 months in a year, the total number of periods is 25 years * 12 months/year = 300 months.

Step 3: Calculate the interest rate per period
The annual interest rate is given as 6.25%, compounded monthly. To find the interest rate per period, we divide the annual interest rate by 12 (the number of compounding periods in a year). Therefore, the interest rate per period is 6.25% / 12 = 0.0625 / 12 = 0.00521 (rounded to 5 decimal places).

Step 4: Calculate the future value of the annuity

PV = PMT * [(1 - (1 + r)^(-n)) / r]
where:
PV = Present Value of the annuity (the total amount to be accumulated)
PMT = Monthly payment ($3000)
r = Interest rate per period (0.00521)
n = Total number of periods (300 months)

Substituting the values into the formula:
PV = $3000 * [(1 - (1 + 0.00521)^(-300)) / 0.00521]

Step 5: Calculate the monthly deposit
To find the monthly deposit required, we need to solve for PMT in the formula:

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

Substituting the values from step 4 into the formula:
PMT = [$3000 * [(1 - (1 + 0.00521)^(-300)) / 0.00521] / [(1 - (1 + 0.00521)^(-300)) / 0.00521]]

Calculating this equation will give you the monthly deposit amount.