Question 1200182: Francine currently has $45,000 in her 401k account at work, and plans to contribute $800 at the end of each month for the next 15 years. How much will she have in the account in 15 years, if the account averages a 6% annual return? Assume monthly compounding.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! she currently has 45000 in her account.
she will contribute an additional 800 at thre end of each month for the next 15 years.
the account averages 6% per year compounded monthly.
you can use a financial calculator to solve this.
the one i use online is at https://arachnoid.com/finance/
the calculator says that you will have 343,089.18 at the end of the 15 year invstment period.
the results are shown below:
your inputs are:
pv = -45000
fv = 0
np = 15 years * 12 months per year = 180 months
pmt = -800 payable at the end of each month.
ir = 6% per year divided by 12 months per year = .5% per month.
calculator comes back with fv = 343,089.18
the present value and the payment per month were negative becaus that is your money that you invested in the account.
the future value is positive because that is what you earned at the end of the 15 years investment period.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Francine currently has $45,000 in her 401k account at work, and plans to contribute $800 at the end of each month for the next 15 years. How much will she have in the account in 15 years, if the account averages a 6% annual return? Assume monthly compounding.
For the $45,000 BEGINNING amount, use the FUTURE VALUE formula of $1:
 , where:  = Accumulated amount, or future value (Unknown, in this case)
 = Present Value||Principal invested||INITIAL amount deposited ($45,000, in this case)
 = Annual Interest rate (6%, or .06, in this case)
 = Number of ANNUAL compounding periods (Monthly, or 12, in this case)
 = Time, in years (15, in this case)
For the monthly $800 contribution, use the formula for the FUTURE VALUE of an ORDINARY ANNUITY:
 , where:  is the future value in the amount of time (years), or the amount that will
be available then (UNKNOWN, in this case)
 is the payment amount ($800, in this case)
is the interest rate, per year (6%, or .06, in this case)
is the number of compounding periods per year (12, in this case)
is the amount of time the money is invested (15, in this case)
You then ADD "A" to FVoa to get the amount in the account after 15 years.
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