# Superannuation Geometric Series Question

• Nov 25th 2010, 03:47 AM
rusdev
Superannuation Geometric Series Question
Qu:
An amount of \$3000 is invested in a superannuation fund at the start of each year for 18 years. The interest at a rate of 9% p.a. is paid half-year.

How much is the investment worth after 18 years?

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I don't understand how you need to adjust the equation for the 9% interest being paid every half a year...
• Nov 25th 2010, 04:18 AM
Wilmer
• Nov 29th 2010, 07:57 PM
dexteronline
Quote:

Originally Posted by rusdev
Qu:
An amount of \$3000 is invested in a superannuation fund at the start of each year for 18 years. The interest at a rate of 9% p.a. is paid half-year.

How much is the investment worth after 18 years?

---------------------

I don't understand how you need to adjust the equation for the 9% interest being paid every half a year...

You are trying to find future value of an annuity due. The plain formula for this is
or
FVAD = R x (1+i) [(1+i)^n - 1]/i

But since we have semiannual compounding we divide i by 2 and multiply n by 2

FVAD = R x (1+i/2) [(1+i/2)^2n - 1]/(i/2)
FVAD = 3000 x (1+9%/2) [(1+9%/2)^36 - 1]/(9%/2)
FVAD = 3000 x (1+4.5%) [(1+4.5%)^36 - 1]/(4.5%)
FVAD = 3000 x (1.045) [(1.045)^36 - 1]/(0.045)
FVAD = 3000 x (1.045) [(1.045)^36 - 1]/(0.045)
FVAD = 3000 x (1.045) [4.8773784614756470522995531708692-1]/0.045
FVAD = 3000 x (1.045) [3.8773784614756470522995531708692]/0.045
FVAD = 3000 x (1.045) [3.8773784614756470522995531708692]/0.045
FVAD = 3000 x (1.045) 86.163965810569934495545626019316