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Question 1099369: Susana started investing $2000 each December 31st since she was 25 years old. Susana is now looking to retire at the end of the year, when she will be 65 years old. How much money does she have in her account if the account paid 8% compounded annually? Round your answer to the nearest dollar.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! using a time value of money calculator:
PV = 0
FV = what you want to find.
PMT = -2000 at the end of each year (negative because you are investing it)
N = number of years = 65 - 25 = 40 years.
i% = interest rate percent per year = 8%
make your inputs and compute FV to get FV = 518,113.0374
the manual formula is shown below:
FUTURE VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
f = (a*((1+r)^n-1))/r
f is the future value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods
in this formula:
f is the future value
a is the payment amount
r is the interest rate per time period (not the percent)
n is the number of time periods.
in your problem:
f is what you want to find.
a is 2000
r is .08
n is 40
the formula becomes:
f = (2000*((1+.08)^40-1))/.08
the result is f = 518,113.0374
the results match, as they should.
when using the calculator, you input the rate percent per time period.
when using the manual formula, you input the rate per time period.
a useful reference on financial formula can be found at https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f3
this reference also includes reference to an online calculator you might find helpful.
that calculator can be found at https://arachnoid.com/finance/
using that calculator, i got f = 518,113.04.
you have to make sure payments are set to end of period.
i made sure i did the same with my own financial calculator.
the manual formula above assumed end of time period payments.
that calculator is the Texas Instruments BA II Plus.
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