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# future value of annuity

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Mr A deposited \$700 at the end of each month of calendar year 2010 in an investment account of 9% annual interest rate. Calculate the future value of the annuity on Dec 31, 2011. Compounding is done on monthly basis.

Mar 19, 2019

#1
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FV=P{[1 + R]^N - 1/ R
FV=700{[1 + 0.09/12]^(2*12) - 1] / (0.09/12)}
FV=700{[1.0075]^24 - 1] / (0.0075)}
FV=700 x {26.188471.......}
FV=\$18,331.93
Note: This balance is on the assumption that 9% is compounded monthly.

Mar 19, 2019
#2
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Mr A deposited 700\$ only through the one year (2010), not through 2 years.

That means: in the year 2010 - 12deposits of 700\$ each; in the year 2011 - 0 new deposits.

Through all the year 2011 amount of money (I mean a capital only) is unchanged and equels 8400\$.

Guest Mar 19, 2019
edited by Guest  Mar 19, 2019
edited by Guest  Mar 19, 2019
edited by Guest  Mar 19, 2019
#3
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Using the same formula the first guest posted for an ordinary annuity

use  n = 12     and R = .09/12 = .0075

FV=P{[1 + R]^N - 1}/ R

FV = 700 {(1.0075)^12 - 1}/(.0075)  = 8755.31  after the first year....

Now this amount gets compound interest monthly for the next 12 months

8755.31 (1+.0075)^12 = \$ 9576.62

Mar 20, 2019