Help needed on superannuation question (1 Viewer)

[EViL.GENiUS]

Hi

I can't solve this question could some one help by posting the solution.

A man is to receive six payments of $500 each, the first payment in a year's time and subsequent payments at two-yearly intervals. He invests each payment at nine per cent per annum. How much will he have immediately after the last payment is made?

Thanks

 

[lolokay]

S = 500 + 500*(1.09)^2 + 500*(1.09)^2 +... 500*(1.09)^10
S(1.09)^2 = 500*(1.09)^2 +... 500*(1.09)^12
S(0.09) = 500*(1.09)^12 - 500
S = [500*(1.09)^12 - 500]/(0.09)
= $10,070

I think

 

[lyounamu]

S = 500 + 500*(1.09)^2 + 500*(1.09)^2 +... 500*(1.09)^10
S(1.09)^2 = 500*(1.09)^2 +... 500*(1.09)^12
S(0.09) = 500*(1.09)^12 - 500
S = [500*(1.09)^12 - 500]/(0.09)
= $10,070

I think

I don't think it can be that much. He is only receiving 6 payments of $500.

My calculation is like this:

500 . (1.09)^10 + 500 . (1.09)^8 + ... + 500 . (1.09)
= 4818.35401... (I used the sum of geometric series)

 

[Aerath]

Hmm, I got what Lyounamu got. But at the same time, I'm not sure we've interpreted the question correctly. =\

 

[lyounamu]

Hmm, I got what Lyounamu got. But at the same time, I'm not sure we've interpreted the question correctly. =\

But the question said 6 payments. Realistically, I don't think it will triple with annual increase of 9%.

 

[lolokay]

S = 500 + 500*(1.09)^2 + 500*(1.09)^2 +... 500*(1.09)^10
S(1.09)^2 = 500*(1.09)^2 +... 500*(1.09)^12
S(0.09) = 500*(1.09)^12 - 500
S = [500*(1.09)^12 - 500]/(0.09)
= $10,070

I think

that was my error
it should be S(1.09²-1) = 500*(1.09)¹² - 500

which gives the answer you guys got

 

[Darrow]

My calculation is like this:

500 . (1.09)^10 + 500 . (1.09)^8 + ... + 500 . (1.09)
= 4818.35401... (I used the sum of geometric series)

Do you mean:
500( 1.09^10) +500(1.09^8) ......+500(1.09^2) +500
= 4818.35
Thats what I did to get your answer

 

[lyounamu]

Do you mean:
500( 1.09^10) +500(1.09^8) ......+500(1.09^2) +500
= 4818.35
Thats what I did to get your answer

Yeah. I just did my question on the calculator and put my working out wrong. I blame my sleeplessness.