Superannuation Question (1 Viewer)

[King2]

Jenny puts aside $20 at the end of each month for 3 year. How much will she have at the end of the 3 years if the investment earns 8.2% p.a., paid monthly?

 

[Starcraftmazter]

$813.16 to the nearest cent.

 

[watatank]

payment each month: 20
number of periods: 36 (3 years)
interest rate: 8.2%/12 = 0.683% = 0.00683

end of first month: 20
end of second: 20*1.00683+ 20 = 20(1+1.00683)
end of third: 20(1+1.00683)*1.00683+ 20 = 20(1+1.00683+1.00683²)

so you can see the pattern...

end of nth month: 20(1 + 1.00683 +1.00683²+....+1.00683^n-1)

so using that info, at the end of 36th month
= 20(1+1.00683 +1.00683²+....+1.00683³⁵)
= 20 * 1 . [1.00683³⁶ - 1) / (1.00683 - 1) ]
= $813.11

hope that helps

 

[Starcraftmazter]

You rounded off your interest rate to 5dp, missing 4sf, and falling 5c short of the correct result.

In real life, the bank would have cheated you by an entire 5 cents - imagine that blasphamy


AFAIK, you are never ever meant to round off, unless specifically instructed, in long calculations such as these.