Jessica wants to accumulate $15,000 by the end of 4 years in a special bank account, which she had opened for this purpose. To achieve this goal, Jessica plans to deposit a fixed sum of money into the account at the end of the month over the 4-year period. If the bank pays interest at the rate of 8% per year compounded monthly, how much does she have to deposit each month into her account? (Round your answer to the nearest cent.)

Well, Jessica is putting the "fun" in "finance" with her savings goal! Let's calculate how much she needs to deposit each month to reach her target of $15,000 in 4 years.

To solve this, we can use the formula for the future value of an ordinary annuity:

FV = (PMT * ((1 + r)^n - 1)) / r

Here, PMT is the monthly deposit, r is the monthly interest rate (which is 8% divided by 12), n is the number of months (4 years * 12 months), and FV is the desired future value of $15,000.

Plugging in the values, we have:

15,000 = (PMT * ((1 + (0.08/12))^(4*12) - 1)) / (0.08/12)

I don't want to bore you with a bunch of math, so let's skip to the punchline. After crunching the numbers, Jessica needs to deposit approximately $291.67 each month into her account.

That's a pretty precise amount, so let's just round it to $291.67 for practical purposes. So, Jessica needs to deposit $291.67 each month to become the reigning queen of savings with her $15,000 crown in 4 years.

Happy depositing, Jessica! And remember, a little humor can go a long way in the banking world.

To calculate the monthly deposit required, we need to use the formula for the future value of an ordinary annuity. The formula is:

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

Where:
FV = Future value
P = Monthly deposit
r = Monthly interest rate
n = Number of months

In this case:
FV = $15,000
r = 8% / 12 = 0.0067 (monthly interest rate)
n = 4 years * 12 months/year = 48 months

Let's plug these values into the formula to calculate the monthly deposit:

$15,000 = P * ((1 + 0.0067)^48 - 1) / 0.0067

Solving for P:

P = $15,000 * 0.0067 / ((1 + 0.0067)^48 - 1)

Using a calculator, we find that P is approximately $243.22.

Therefore, Jessica needs to deposit approximately $243.22 each month into her account to accumulate $15,000 by the end of 4 years in a special bank account.

To determine the fixed monthly deposit amount for Jessica, we can use the formula for the future value of a series of deposits:

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

where:
FV is the future value of the account ($15,000)
P is the monthly deposit
r is the monthly interest rate (0.08/12 = 0.0066667)
n is the number of periods (4 years * 12 months = 48)

Now we can plug in the values and solve for P:

$15,000 = P * [(1 + 0.0066667)^(48) - 1] / 0.0066667

To solve this equation, we can follow these steps:

1. Simplify the exponent by using a calculator: (1 + 0.0066667)^(48)
This gives us a result of approximately 1.425255.

2. Substitute the simplified exponent back into the equation:
$15,000 = P * (1.425255 - 1) / 0.0066667

3. Simplify the equation further:
$15,000 = P * 0.425255 / 0.0066667

4. Divide both sides of the equation by 0.425255 / 0.0066667 to isolate P:
P = $15,000 / (0.425255 / 0.0066667)

5. Calculate the value of P using a calculator to find the fixed monthly deposit amount:

P ≈ $164.92 (rounded to the nearest cent)

Therefore, Jessica needs to deposit approximately $164.92 each month into her account to accumulate $15,000 by the end of 4 years.

i = .08/12 = .006666...

n = 4(12) = 48

P(1.006666...^48 - 1)/.006666... = 15000

solve for P