Difficult Superannuation Problem (1 Viewer)

[Drewk]

Lee invests $100 at the beginning of each year in superannuation. Her fund pays 9%pa. and the interest compounds monthly. Find the total value of her investment including interest at the end of 20 years





A: $5840.77

 

[Drongoski]

Since this is a 2U question, maybe I can do this one.


Interest rate per compounding period is 0.75% = 0.0075 and each year, interest is compounded 12 times.
At the end of 20 yrs = 240 months:

1st $100 becomes $100 x [1.0075^12]^20

2nd $100 becomes $100 x [1.0075^12]^19

. . . .

2nd last $100 becomes $100 x [1.0075^12]^2

Final $100 becomes $100 x [1.0075^12]^1

.: total at end of 20 years = sum of all above

= $100 x [a geometric sum: 1st term = 1.0075^12, number of terms = 20 and common ratio = 1.0075^12]



= $5840.77

 

[SharkeyBoy]

It's compounded monthly, so 9%/12 + 1 = 1.0075
He puts in $100 every year at the beginning and so, by the time next year comes, it would have been compounded 12 times.
Therefore:
A1 = 100 (1.0075)^12*20
= 100 (1.0075)*240
A2 = 100 (1.0075)*228
A3 = 100 (1.0075)*216
...
...
A19 = 100 (1.0075)*24
A20 = 100 (1.0075)*12

The sum of these 20 years is: 100 (1.0075^240 + 1.0075^228 + .... + 1.0075^12)
the part in brackets is a geometric series where a = (1.0075^12), r = 1..075^12 and there are 2 terms

Therefore S20 = 100 [ 1.0075^12(1.0075^12)^20 - 1 ] / [ .0075^12]
= $5940.77 which means that either I'm slightly off, or you had a typo
Hope it helps either way

 

[SharkeyBoy]

Maybe I can do this one.

ooh sorry! Didn't see your post!

 

[Drongoski]

ooh sorry! Didn't see your post!

That's alright. I was just being too slow inputting my solution!

 

[Drewk]

Thanks