SOLUTION: An executive prepares for retirement by depositing $4000 into an annuity each year for 10 years. The annuity earns 6.4% per year. Find the future value of the annuity at the end of
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Question 1096475: An executive prepares for retirement by depositing $4000 into an annuity each year for 10 years. The annuity earns 6.4% per year. Find the future value of the annuity at the end of 10 years. (Round your final answer to two decimal places.) I have already tried 4000(((1+(.064/12))^120-1)/(.064/12))=A and it isn't working. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! you need to assume whether your payments are made at the end of the time period or at the beginning of the time period.
that's a first step.
you also need to know how many compounding periods a year are assumed.
you state that you make one payment of 4000 each year.
that means 1 compounding period per year, unless your problem states 12 compounding periods per year.
here's some answers based on different assumptions.
usually the number of payments per year is aligned with the number of compounding periods per year so i'll assume that's the case.
the first result assumes annual compounding with annual payments at the end of each year.
the second result assumes annual compounding with annual payments at the beginning of each year.
with these assumptions, the number of time periods is 10 and the interest rate percent time period is 6.4.
the third result assumes monthly compounding with monthly payments at the end of each month.
the fourth result assumes monthly compounding with monthly payments at the beginning of each month.
with these assumptions, the number of time periods is 10 * 12 = 120 and the interest rate percent per time period is 6.4 / 12 = .533333333.
the general rule is that the number of time periods is equal to the number of years * the number of compounding periods per year and the interest rate per time period is the interest rate per year divided by the number of compounding periods per year.
when you use the calculator, you use interest rate percent.
when you use the formulas, you use interest rate, which is the interest rate percent divided by 100.
the formulas in the reference that you would need to use for this type of problem are:
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
and:
FUTURE VALUE OF AN ANNUITY WITH BEGINNING OF TIME PERIOD PAYMENTS
f = ((a*(1+r)^n-1)/r)*(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
the time periods used are the key to solving the problems correctly, along with assumption about end of period payments or beginning of period payments.
look for the future value in the calculator calculations.
one of those results should be the one you are looking for.
go through the formulas and see if you can duplicate the calculator results.
