SOLUTION: This one has me stumped:
The owner of a café plans to open a second location in 8 years. She purchases an annuity that pays 8.5% interest compounded annually. If the payment i
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-> SOLUTION: This one has me stumped:
The owner of a café plans to open a second location in 8 years. She purchases an annuity that pays 8.5% interest compounded annually. If the payment i
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Question 970931: This one has me stumped:
The owner of a café plans to open a second location in 8 years. She purchases an annuity that pays 8.5% interest compounded annually. If the payment is $3,450 a year, find the future value of the annuity in 8 years. Round your answer to the nearest cent.
Thanks! Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! annuity pays 8.5% interest compounded annually.
the payment is 3450 each year.
find the future value of the annuity in 8 years.
fv = what you want to find
pv = 0
pmt = 3450 each year.
interest rate percent = 8.5% per year compounded annually.
the only question is whether she makes the payment at the beginning of each year or at the end of each year.
without knowing that, we'll do both.
the formula for the future value of an annuity is in the following link.
that link also includes a calculator where you can test your results.
look for the formula for fv = .......
there are two formulas.
the one on the left is for payments at the beginning of the time period.
the one on the right is for payments at the end of the time period.
the easy way to do it is to use the formula for payments at the end of the time period and then multiply the result by 1 + r.
this will give you the future value for payments at the beginning of the time period.
you need to determine what the time periods are and translate the time periods you are given to the number of time periods reqquired.
the formula is based on compounding periods per year.
time periods = y*c where y is number of years and c is number of compounding periods per year.
interesst rate per time period = r / c where r is the interest rate per year and c is the number of compounding periods per year.
in this problem, the time periods are in years and the interest rate is in years so no adjustment is necessary.
the calculator uses interest rate percent.
the formulas use interest rate.
convert from interest rate percent to interest rate by dividing the interest rate percent by 100.
8.5% interest rate percent per year is the same as .085 per year interest rate per year.
i used the calculator and the formulas and got the same answers.
the calculator results are shown below:
the first one assumes payments made at the beginning of the year.
the second one assumes payments made at the end of the year.
if you take the PMABOY future value number and divide it by the PMAEOY future value number, you will see that BOY is 1.085 * EOY results.
when you usde the calculator to calculate FV, you do the following.
enter 3450 for present value.
leave future value blank
enter 8 for number of payments
enter 3450 for payment amount
enter 8.5 for interest rate per period percent.
select payment at beginning or end of year, whichever you want.
left click mouse on FV button.
