Applications of Sequences and Series Q (1 Viewer)

[Libbster]

John invests $500 in an investment fund at the beginning of every two months. It earns 6%pa compounded monthly How much will be in the account at the end of 10 years.

Would I be correct in saying that there are 60 payment periods but 120 compounding periods? Would I set it up like this, or am I just going completely crazy? If you work it out, can you please post up your answer, because I don't have answers to this particular past paper!

6/12= 0.5


U1 = 500 (1.005)^2
U2 = 500 (1.005)^4
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U60 = 500 (1.005)^120

 

[Libbster]

Anyone or anything?! lol

 

[withoutaface]

T1= $500
T2= $500*1.005
T3= ($500*1.005)*1.005+$500
...
Tn=$500(1.005^(n-1)+1.005^(n-3)...+ either 1.005 (for even n) or 1 (for odd n))

∴ T121 = 500*(1.005^2*60-1)/(1.005²-1)

At least that should be close to the answer, it's been a while since I've touched sequences and series.

 

[Libbster]

i haven't done these types of q's for ages, so i've forgotten. But doesn't he pay 500 every two months, but interest in monthly so wouldn't the first 500 get compounded twice? Can someone please explain?

 

[Libbster]

Just ignore the my crazy maths working in the first part of my post, i was thinking of superannuation. Whoops!

 

[Libbster]

i understand now. Thankyou!