SOLUTION: An individual earns an extra $2000 each year and places this money at the end of each year into an Individual Retirement Account (IRA) in which both the original earnings and the i
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Question 1140368: An individual earns an extra $2000 each year and places this money at the end of each year into an Individual Retirement Account (IRA) in which both the original earnings and the interest in the account are not subject to taxation. If the account has an annual interest rate of 10.3% compounded annually, how much is in the account at the end of 40 years? (Round your answer to the nearest cent.)
You can put this solution on YOUR website! he's putting 2000 at the end of each year for 40 years at 10.3% interest rate per year compounded annually.
using the TI-BA-II financial calculator (Texas Instruments), i input the following and get the following result.
number of time periods = 40
interest rate per time period = 10.3%
present value = 0
future value = 0
payment each time period = -2000 (negative because it's money going out).
i have the calculator compute the future value.
it tells me that the future value is equal to 960,553.625 dollars.
the future value is what i invest at the end of each year plus interest earned on that investment plus interest earned on the interest earned on that investment.
you can do something similar with the following online financial calculator.
the particular formula that would be used for your problem 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, you use the interest rate, not the percent.
rate is equal to percent / 100.
you also do not make the payment negative.
everything is positive in this formula.
make your entries in your calculator using the parentheses exactly as is.
for your problem, your inputs should look like this:
f = (a*((1+r)^n-1))/r becomes:
f= (2000*((1+.103)^40-1))/.103
you should get f = 960553.625 as i just did, using my TI-84 Plus calculator.
